Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.34292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.48929 | 1.43719 | 0.718596 | − | 0.695428i | \(-0.244785\pi\) | ||||
0.718596 | + | 0.695428i | \(0.244785\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.48929 | 1.01625 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.19656 | 1.06552 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.48929 | 0.718596 | ||||||||
\(13\) | 2.48929 | 0.690404 | 0.345202 | − | 0.938528i | \(-0.387810\pi\) | ||||
0.345202 | + | 0.938528i | \(0.387810\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −2.48929 | −0.642732 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.19656 | 1.26035 | 0.630175 | − | 0.776453i | \(-0.282983\pi\) | ||||
0.630175 | + | 0.776453i | \(0.282983\pi\) | |||||||
\(18\) | 3.19656 | 0.753436 | ||||||||
\(19\) | 0.707269 | 0.162259 | 0.0811293 | − | 0.996704i | \(-0.474147\pi\) | ||||
0.0811293 | + | 0.996704i | \(0.474147\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 2.48929 | 0.543207 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.17513 | 1.07909 | 0.539545 | − | 0.841957i | \(-0.318596\pi\) | ||||
0.539545 | + | 0.841957i | \(0.318596\pi\) | |||||||
\(24\) | 2.48929 | 0.508124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.48929 | 0.488190 | ||||||||
\(27\) | 0.489289 | 0.0941636 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −2.39312 | −0.444390 | −0.222195 | − | 0.975002i | \(-0.571322\pi\) | ||||
−0.222195 | + | 0.975002i | \(0.571322\pi\) | |||||||
\(30\) | −2.48929 | −0.454480 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.19656 | 0.891202 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 3.19656 | 0.532760 | ||||||||
\(37\) | 7.37169 | 1.21190 | 0.605949 | − | 0.795503i | \(-0.292793\pi\) | ||||
0.605949 | + | 0.795503i | \(0.292793\pi\) | |||||||
\(38\) | 0.707269 | 0.114734 | ||||||||
\(39\) | 6.19656 | 0.992243 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −4.97858 | −0.777523 | −0.388762 | − | 0.921338i | \(-0.627097\pi\) | ||||
−0.388762 | + | 0.921338i | \(0.627097\pi\) | |||||||
\(42\) | 2.48929 | 0.384106 | ||||||||
\(43\) | −9.15371 | −1.39593 | −0.697964 | − | 0.716133i | \(-0.745910\pi\) | ||||
−0.697964 | + | 0.716133i | \(0.745910\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.19656 | −0.476515 | ||||||||
\(46\) | 5.17513 | 0.763032 | ||||||||
\(47\) | −5.37169 | −0.783542 | −0.391771 | − | 0.920063i | \(-0.628137\pi\) | ||||
−0.391771 | + | 0.920063i | \(0.628137\pi\) | |||||||
\(48\) | 2.48929 | 0.359298 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 12.9357 | 1.81136 | ||||||||
\(52\) | 2.48929 | 0.345202 | ||||||||
\(53\) | −1.19656 | −0.164360 | −0.0821799 | − | 0.996618i | \(-0.526188\pi\) | ||||
−0.0821799 | + | 0.996618i | \(0.526188\pi\) | |||||||
\(54\) | 0.489289 | 0.0665837 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 1.76060 | 0.233197 | ||||||||
\(58\) | −2.39312 | −0.314231 | ||||||||
\(59\) | 3.29273 | 0.428677 | 0.214339 | − | 0.976759i | \(-0.431240\pi\) | ||||
0.214339 | + | 0.976759i | \(0.431240\pi\) | |||||||
\(60\) | −2.48929 | −0.321366 | ||||||||
\(61\) | 7.78202 | 0.996386 | 0.498193 | − | 0.867066i | \(-0.333997\pi\) | ||||
0.498193 | + | 0.867066i | \(0.333997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.19656 | 0.402728 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.48929 | −0.308758 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.58967 | −0.927226 | −0.463613 | − | 0.886038i | \(-0.653447\pi\) | ||||
−0.463613 | + | 0.886038i | \(0.653447\pi\) | |||||||
\(68\) | 5.19656 | 0.630175 | ||||||||
\(69\) | 12.8824 | 1.55086 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 12.1751 | 1.44492 | 0.722461 | − | 0.691411i | \(-0.243011\pi\) | ||||
0.722461 | + | 0.691411i | \(0.243011\pi\) | |||||||
\(72\) | 3.19656 | 0.376718 | ||||||||
\(73\) | −0.175135 | −0.0204980 | −0.0102490 | − | 0.999947i | \(-0.503262\pi\) | ||||
−0.0102490 | + | 0.999947i | \(0.503262\pi\) | |||||||
\(74\) | 7.37169 | 0.856942 | ||||||||
\(75\) | 2.48929 | 0.287438 | ||||||||
\(76\) | 0.707269 | 0.0811293 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.19656 | 0.701622 | ||||||||
\(79\) | 1.97858 | 0.222607 | 0.111304 | − | 0.993786i | \(-0.464497\pi\) | ||||
0.111304 | + | 0.993786i | \(0.464497\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −8.37169 | −0.930188 | ||||||||
\(82\) | −4.97858 | −0.549792 | ||||||||
\(83\) | 4.48929 | 0.492763 | 0.246382 | − | 0.969173i | \(-0.420758\pi\) | ||||
0.246382 | + | 0.969173i | \(0.420758\pi\) | |||||||
\(84\) | 2.48929 | 0.271604 | ||||||||
\(85\) | −5.19656 | −0.563646 | ||||||||
\(86\) | −9.15371 | −0.987070 | ||||||||
\(87\) | −5.95715 | −0.638674 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.978577 | −0.103729 | −0.0518645 | − | 0.998654i | \(-0.516516\pi\) | ||||
−0.0518645 | + | 0.998654i | \(0.516516\pi\) | |||||||
\(90\) | −3.19656 | −0.336947 | ||||||||
\(91\) | 2.48929 | 0.260948 | ||||||||
\(92\) | 5.17513 | 0.539545 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.37169 | −0.554048 | ||||||||
\(95\) | −0.707269 | −0.0725643 | ||||||||
\(96\) | 2.48929 | 0.254062 | ||||||||
\(97\) | 4.17513 | 0.423921 | 0.211960 | − | 0.977278i | \(-0.432015\pi\) | ||||
0.211960 | + | 0.977278i | \(0.432015\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −6.48929 | −0.645708 | −0.322854 | − | 0.946449i | \(-0.604642\pi\) | ||||
−0.322854 | + | 0.946449i | \(0.604642\pi\) | |||||||
\(102\) | 12.9357 | 1.28083 | ||||||||
\(103\) | 3.78202 | 0.372653 | 0.186327 | − | 0.982488i | \(-0.440342\pi\) | ||||
0.186327 | + | 0.982488i | \(0.440342\pi\) | |||||||
\(104\) | 2.48929 | 0.244095 | ||||||||
\(105\) | −2.48929 | −0.242930 | ||||||||
\(106\) | −1.19656 | −0.116220 | ||||||||
\(107\) | −4.21798 | −0.407768 | −0.203884 | − | 0.978995i | \(-0.565356\pi\) | ||||
−0.203884 | + | 0.978995i | \(0.565356\pi\) | |||||||
\(108\) | 0.489289 | 0.0470818 | ||||||||
\(109\) | −9.37169 | −0.897645 | −0.448823 | − | 0.893621i | \(-0.648157\pi\) | ||||
−0.448823 | + | 0.893621i | \(0.648157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.3503 | 1.74173 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 10.5897 | 0.996193 | 0.498096 | − | 0.867122i | \(-0.334033\pi\) | ||||
0.498096 | + | 0.867122i | \(0.334033\pi\) | |||||||
\(114\) | 1.76060 | 0.164895 | ||||||||
\(115\) | −5.17513 | −0.482584 | ||||||||
\(116\) | −2.39312 | −0.222195 | ||||||||
\(117\) | 7.95715 | 0.735639 | ||||||||
\(118\) | 3.29273 | 0.303120 | ||||||||
\(119\) | 5.19656 | 0.476368 | ||||||||
\(120\) | −2.48929 | −0.227240 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 7.78202 | 0.704551 | ||||||||
\(123\) | −12.3931 | −1.11745 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.19656 | 0.284772 | ||||||||
\(127\) | 2.82487 | 0.250666 | 0.125333 | − | 0.992115i | \(-0.460000\pi\) | ||||
0.125333 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −22.7862 | −2.00622 | ||||||||
\(130\) | −2.48929 | −0.218325 | ||||||||
\(131\) | −15.8181 | −1.38204 | −0.691018 | − | 0.722837i | \(-0.742838\pi\) | ||||
−0.691018 | + | 0.722837i | \(0.742838\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.707269 | 0.0613280 | ||||||||
\(134\) | −7.58967 | −0.655648 | ||||||||
\(135\) | −0.489289 | −0.0421113 | ||||||||
\(136\) | 5.19656 | 0.445601 | ||||||||
\(137\) | 17.1323 | 1.46371 | 0.731855 | − | 0.681460i | \(-0.238655\pi\) | ||||
0.731855 | + | 0.681460i | \(0.238655\pi\) | |||||||
\(138\) | 12.8824 | 1.09662 | ||||||||
\(139\) | 16.4721 | 1.39714 | 0.698572 | − | 0.715540i | \(-0.253819\pi\) | ||||
0.698572 | + | 0.715540i | \(0.253819\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −13.3717 | −1.12610 | ||||||||
\(142\) | 12.1751 | 1.02171 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.19656 | 0.266380 | ||||||||
\(145\) | 2.39312 | 0.198737 | ||||||||
\(146\) | −0.175135 | −0.0144943 | ||||||||
\(147\) | 2.48929 | 0.205313 | ||||||||
\(148\) | 7.37169 | 0.605949 | ||||||||
\(149\) | −14.9357 | −1.22358 | −0.611791 | − | 0.791019i | \(-0.709551\pi\) | ||||
−0.611791 | + | 0.791019i | \(0.709551\pi\) | |||||||
\(150\) | 2.48929 | 0.203250 | ||||||||
\(151\) | −13.1323 | −1.06869 | −0.534345 | − | 0.845266i | \(-0.679442\pi\) | ||||
−0.534345 | + | 0.845266i | \(0.679442\pi\) | |||||||
\(152\) | 0.707269 | 0.0573671 | ||||||||
\(153\) | 16.6111 | 1.34293 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.19656 | 0.496122 | ||||||||
\(157\) | −8.88240 | −0.708893 | −0.354446 | − | 0.935076i | \(-0.615331\pi\) | ||||
−0.354446 | + | 0.935076i | \(0.615331\pi\) | |||||||
\(158\) | 1.97858 | 0.157407 | ||||||||
\(159\) | −2.97858 | −0.236217 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 5.17513 | 0.407858 | ||||||||
\(162\) | −8.37169 | −0.657742 | ||||||||
\(163\) | 10.5254 | 0.824413 | 0.412207 | − | 0.911090i | \(-0.364758\pi\) | ||||
0.412207 | + | 0.911090i | \(0.364758\pi\) | |||||||
\(164\) | −4.97858 | −0.388762 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.48929 | 0.348436 | ||||||||
\(167\) | 22.5254 | 1.74307 | 0.871534 | − | 0.490335i | \(-0.163126\pi\) | ||||
0.871534 | + | 0.490335i | \(0.163126\pi\) | |||||||
\(168\) | 2.48929 | 0.192053 | ||||||||
\(169\) | −6.80344 | −0.523342 | ||||||||
\(170\) | −5.19656 | −0.398558 | ||||||||
\(171\) | 2.26083 | 0.172890 | ||||||||
\(172\) | −9.15371 | −0.697964 | ||||||||
\(173\) | −13.5640 | −1.03125 | −0.515627 | − | 0.856813i | \(-0.672441\pi\) | ||||
−0.515627 | + | 0.856813i | \(0.672441\pi\) | |||||||
\(174\) | −5.95715 | −0.451611 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.19656 | 0.616091 | ||||||||
\(178\) | −0.978577 | −0.0733475 | ||||||||
\(179\) | 26.3503 | 1.96951 | 0.984756 | − | 0.173943i | \(-0.0556507\pi\) | ||||
0.984756 | + | 0.173943i | \(0.0556507\pi\) | |||||||
\(180\) | −3.19656 | −0.238257 | ||||||||
\(181\) | 1.48508 | 0.110385 | 0.0551925 | − | 0.998476i | \(-0.482423\pi\) | ||||
0.0551925 | + | 0.998476i | \(0.482423\pi\) | |||||||
\(182\) | 2.48929 | 0.184518 | ||||||||
\(183\) | 19.3717 | 1.43200 | ||||||||
\(184\) | 5.17513 | 0.381516 | ||||||||
\(185\) | −7.37169 | −0.541978 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.37169 | −0.391771 | ||||||||
\(189\) | 0.489289 | 0.0355905 | ||||||||
\(190\) | −0.707269 | −0.0513107 | ||||||||
\(191\) | 10.1966 | 0.737797 | 0.368899 | − | 0.929470i | \(-0.379735\pi\) | ||||
0.368899 | + | 0.929470i | \(0.379735\pi\) | |||||||
\(192\) | 2.48929 | 0.179649 | ||||||||
\(193\) | −10.9828 | −0.790558 | −0.395279 | − | 0.918561i | \(-0.629352\pi\) | ||||
−0.395279 | + | 0.918561i | \(0.629352\pi\) | |||||||
\(194\) | 4.17513 | 0.299757 | ||||||||
\(195\) | −6.19656 | −0.443745 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 27.5040 | 1.95958 | 0.979789 | − | 0.200035i | \(-0.0641056\pi\) | ||||
0.979789 | + | 0.200035i | \(0.0641056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.56404 | 0.536201 | 0.268100 | − | 0.963391i | \(-0.413604\pi\) | ||||
0.268100 | + | 0.963391i | \(0.413604\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −18.8929 | −1.33260 | ||||||||
\(202\) | −6.48929 | −0.456585 | ||||||||
\(203\) | −2.39312 | −0.167964 | ||||||||
\(204\) | 12.9357 | 0.905682 | ||||||||
\(205\) | 4.97858 | 0.347719 | ||||||||
\(206\) | 3.78202 | 0.263506 | ||||||||
\(207\) | 16.5426 | 1.14979 | ||||||||
\(208\) | 2.48929 | 0.172601 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.48929 | −0.171777 | ||||||||
\(211\) | −20.7862 | −1.43098 | −0.715492 | − | 0.698621i | \(-0.753797\pi\) | ||||
−0.715492 | + | 0.698621i | \(0.753797\pi\) | |||||||
\(212\) | −1.19656 | −0.0821799 | ||||||||
\(213\) | 30.3074 | 2.07663 | ||||||||
\(214\) | −4.21798 | −0.288335 | ||||||||
\(215\) | 9.15371 | 0.624278 | ||||||||
\(216\) | 0.489289 | 0.0332919 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.37169 | −0.634731 | ||||||||
\(219\) | −0.435961 | −0.0294595 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.9357 | 0.870151 | ||||||||
\(222\) | 18.3503 | 1.23159 | ||||||||
\(223\) | 16.7606 | 1.12237 | 0.561186 | − | 0.827690i | \(-0.310345\pi\) | ||||
0.561186 | + | 0.827690i | \(0.310345\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 3.19656 | 0.213104 | ||||||||
\(226\) | 10.5897 | 0.704415 | ||||||||
\(227\) | −13.3717 | −0.887510 | −0.443755 | − | 0.896148i | \(-0.646354\pi\) | ||||
−0.443755 | + | 0.896148i | \(0.646354\pi\) | |||||||
\(228\) | 1.76060 | 0.116598 | ||||||||
\(229\) | −4.13229 | −0.273069 | −0.136535 | − | 0.990635i | \(-0.543597\pi\) | ||||
−0.136535 | + | 0.990635i | \(0.543597\pi\) | |||||||
\(230\) | −5.17513 | −0.341238 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.39312 | −0.157116 | ||||||||
\(233\) | 5.21798 | 0.341841 | 0.170921 | − | 0.985285i | \(-0.445326\pi\) | ||||
0.170921 | + | 0.985285i | \(0.445326\pi\) | |||||||
\(234\) | 7.95715 | 0.520175 | ||||||||
\(235\) | 5.37169 | 0.350411 | ||||||||
\(236\) | 3.29273 | 0.214339 | ||||||||
\(237\) | 4.92525 | 0.319929 | ||||||||
\(238\) | 5.19656 | 0.336843 | ||||||||
\(239\) | −30.3032 | −1.96015 | −0.980076 | − | 0.198623i | \(-0.936353\pi\) | ||||
−0.980076 | + | 0.198623i | \(0.936353\pi\) | |||||||
\(240\) | −2.48929 | −0.160683 | ||||||||
\(241\) | 11.4145 | 0.735275 | 0.367638 | − | 0.929969i | \(-0.380167\pi\) | ||||
0.367638 | + | 0.929969i | \(0.380167\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.3074 | −1.43102 | ||||||||
\(244\) | 7.78202 | 0.498193 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −12.3931 | −0.790156 | ||||||||
\(247\) | 1.76060 | 0.112024 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.1751 | 0.708195 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −12.7606 | −0.805442 | −0.402721 | − | 0.915323i | \(-0.631935\pi\) | ||||
−0.402721 | + | 0.915323i | \(0.631935\pi\) | |||||||
\(252\) | 3.19656 | 0.201364 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.82487 | 0.177248 | ||||||||
\(255\) | −12.9357 | −0.810067 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.58967 | −0.223918 | −0.111959 | − | 0.993713i | \(-0.535712\pi\) | ||||
−0.111959 | + | 0.993713i | \(0.535712\pi\) | |||||||
\(258\) | −22.7862 | −1.41861 | ||||||||
\(259\) | 7.37169 | 0.458055 | ||||||||
\(260\) | −2.48929 | −0.154379 | ||||||||
\(261\) | −7.64973 | −0.473506 | ||||||||
\(262\) | −15.8181 | −0.977248 | ||||||||
\(263\) | 2.63252 | 0.162328 | 0.0811640 | − | 0.996701i | \(-0.474136\pi\) | ||||
0.0811640 | + | 0.996701i | \(0.474136\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.19656 | 0.0735039 | ||||||||
\(266\) | 0.707269 | 0.0433654 | ||||||||
\(267\) | −2.43596 | −0.149078 | ||||||||
\(268\) | −7.58967 | −0.463613 | ||||||||
\(269\) | 12.8996 | 0.786503 | 0.393252 | − | 0.919431i | \(-0.371350\pi\) | ||||
0.393252 | + | 0.919431i | \(0.371350\pi\) | |||||||
\(270\) | −0.489289 | −0.0297772 | ||||||||
\(271\) | −8.93573 | −0.542807 | −0.271404 | − | 0.962466i | \(-0.587488\pi\) | ||||
−0.271404 | + | 0.962466i | \(0.587488\pi\) | |||||||
\(272\) | 5.19656 | 0.315088 | ||||||||
\(273\) | 6.19656 | 0.375033 | ||||||||
\(274\) | 17.1323 | 1.03500 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.8824 | 0.775430 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | 16.4721 | 0.987929 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 20.5212 | 1.22419 | 0.612096 | − | 0.790784i | \(-0.290327\pi\) | ||||
0.612096 | + | 0.790784i | \(0.290327\pi\) | |||||||
\(282\) | −13.3717 | −0.796273 | ||||||||
\(283\) | −0.681635 | −0.0405190 | −0.0202595 | − | 0.999795i | \(-0.506449\pi\) | ||||
−0.0202595 | + | 0.999795i | \(0.506449\pi\) | |||||||
\(284\) | 12.1751 | 0.722461 | ||||||||
\(285\) | −1.76060 | −0.104289 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.97858 | −0.293876 | ||||||||
\(288\) | 3.19656 | 0.188359 | ||||||||
\(289\) | 10.0042 | 0.588483 | ||||||||
\(290\) | 2.39312 | 0.140529 | ||||||||
\(291\) | 10.3931 | 0.609255 | ||||||||
\(292\) | −0.175135 | −0.0102490 | ||||||||
\(293\) | −19.4250 | −1.13482 | −0.567411 | − | 0.823435i | \(-0.692055\pi\) | ||||
−0.567411 | + | 0.823435i | \(0.692055\pi\) | |||||||
\(294\) | 2.48929 | 0.145178 | ||||||||
\(295\) | −3.29273 | −0.191710 | ||||||||
\(296\) | 7.37169 | 0.428471 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.9357 | −0.865204 | ||||||||
\(299\) | 12.8824 | 0.745009 | ||||||||
\(300\) | 2.48929 | 0.143719 | ||||||||
\(301\) | −9.15371 | −0.527611 | ||||||||
\(302\) | −13.1323 | −0.755678 | ||||||||
\(303\) | −16.1537 | −0.928007 | ||||||||
\(304\) | 0.707269 | 0.0405647 | ||||||||
\(305\) | −7.78202 | −0.445597 | ||||||||
\(306\) | 16.6111 | 0.949593 | ||||||||
\(307\) | 14.1923 | 0.810000 | 0.405000 | − | 0.914317i | \(-0.367272\pi\) | ||||
0.405000 | + | 0.914317i | \(0.367272\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.41454 | 0.535574 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.8929 | −1.63837 | −0.819183 | − | 0.573533i | \(-0.805573\pi\) | ||||
−0.819183 | + | 0.573533i | \(0.805573\pi\) | |||||||
\(312\) | 6.19656 | 0.350811 | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | −8.88240 | −0.501263 | ||||||||
\(315\) | −3.19656 | −0.180106 | ||||||||
\(316\) | 1.97858 | 0.111304 | ||||||||
\(317\) | 7.97437 | 0.447885 | 0.223943 | − | 0.974602i | \(-0.428107\pi\) | ||||
0.223943 | + | 0.974602i | \(0.428107\pi\) | |||||||
\(318\) | −2.97858 | −0.167030 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −10.4998 | −0.586040 | ||||||||
\(322\) | 5.17513 | 0.288399 | ||||||||
\(323\) | 3.67536 | 0.204503 | ||||||||
\(324\) | −8.37169 | −0.465094 | ||||||||
\(325\) | 2.48929 | 0.138081 | ||||||||
\(326\) | 10.5254 | 0.582948 | ||||||||
\(327\) | −23.3288 | −1.29009 | ||||||||
\(328\) | −4.97858 | −0.274896 | ||||||||
\(329\) | −5.37169 | −0.296151 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.62831 | 0.474255 | 0.237127 | − | 0.971479i | \(-0.423794\pi\) | ||||
0.237127 | + | 0.971479i | \(0.423794\pi\) | |||||||
\(332\) | 4.48929 | 0.246382 | ||||||||
\(333\) | 23.5640 | 1.29130 | ||||||||
\(334\) | 22.5254 | 1.23254 | ||||||||
\(335\) | 7.58967 | 0.414668 | ||||||||
\(336\) | 2.48929 | 0.135802 | ||||||||
\(337\) | −7.80344 | −0.425081 | −0.212540 | − | 0.977152i | \(-0.568174\pi\) | ||||
−0.212540 | + | 0.977152i | \(0.568174\pi\) | |||||||
\(338\) | −6.80344 | −0.370058 | ||||||||
\(339\) | 26.3608 | 1.43172 | ||||||||
\(340\) | −5.19656 | −0.281823 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.26083 | 0.122251 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −9.15371 | −0.493535 | ||||||||
\(345\) | −12.8824 | −0.693565 | ||||||||
\(346\) | −13.5640 | −0.729207 | ||||||||
\(347\) | 27.1966 | 1.45999 | 0.729994 | − | 0.683454i | \(-0.239523\pi\) | ||||
0.729994 | + | 0.683454i | \(0.239523\pi\) | |||||||
\(348\) | −5.95715 | −0.319337 | ||||||||
\(349\) | −28.0533 | −1.50166 | −0.750830 | − | 0.660495i | \(-0.770346\pi\) | ||||
−0.750830 | + | 0.660495i | \(0.770346\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 1.21798 | 0.0650110 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.5254 | 0.666660 | 0.333330 | − | 0.942810i | \(-0.391828\pi\) | ||||
0.333330 | + | 0.942810i | \(0.391828\pi\) | |||||||
\(354\) | 8.19656 | 0.435642 | ||||||||
\(355\) | −12.1751 | −0.646189 | ||||||||
\(356\) | −0.978577 | −0.0518645 | ||||||||
\(357\) | 12.9357 | 0.684632 | ||||||||
\(358\) | 26.3503 | 1.39266 | ||||||||
\(359\) | −21.3461 | −1.12660 | −0.563301 | − | 0.826252i | \(-0.690469\pi\) | ||||
−0.563301 | + | 0.826252i | \(0.690469\pi\) | |||||||
\(360\) | −3.19656 | −0.168473 | ||||||||
\(361\) | −18.4998 | −0.973672 | ||||||||
\(362\) | 1.48508 | 0.0780540 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.48929 | 0.130474 | ||||||||
\(365\) | 0.175135 | 0.00916697 | ||||||||
\(366\) | 19.3717 | 1.01257 | ||||||||
\(367\) | 24.7178 | 1.29026 | 0.645128 | − | 0.764074i | \(-0.276804\pi\) | ||||
0.645128 | + | 0.764074i | \(0.276804\pi\) | |||||||
\(368\) | 5.17513 | 0.269773 | ||||||||
\(369\) | −15.9143 | −0.828466 | ||||||||
\(370\) | −7.37169 | −0.383236 | ||||||||
\(371\) | −1.19656 | −0.0621222 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.9185 | −0.668896 | −0.334448 | − | 0.942414i | \(-0.608550\pi\) | ||||
−0.334448 | + | 0.942414i | \(0.608550\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.48929 | −0.128546 | ||||||||
\(376\) | −5.37169 | −0.277024 | ||||||||
\(377\) | −5.95715 | −0.306809 | ||||||||
\(378\) | 0.489289 | 0.0251663 | ||||||||
\(379\) | 35.9227 | 1.84523 | 0.922613 | − | 0.385726i | \(-0.126049\pi\) | ||||
0.922613 | + | 0.385726i | \(0.126049\pi\) | |||||||
\(380\) | −0.707269 | −0.0362821 | ||||||||
\(381\) | 7.03190 | 0.360255 | ||||||||
\(382\) | 10.1966 | 0.521701 | ||||||||
\(383\) | 11.6325 | 0.594394 | 0.297197 | − | 0.954816i | \(-0.403948\pi\) | ||||
0.297197 | + | 0.954816i | \(0.403948\pi\) | |||||||
\(384\) | 2.48929 | 0.127031 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.9828 | −0.559009 | ||||||||
\(387\) | −29.2604 | −1.48739 | ||||||||
\(388\) | 4.17513 | 0.211960 | ||||||||
\(389\) | −25.2860 | −1.28205 | −0.641026 | − | 0.767520i | \(-0.721491\pi\) | ||||
−0.641026 | + | 0.767520i | \(0.721491\pi\) | |||||||
\(390\) | −6.19656 | −0.313775 | ||||||||
\(391\) | 26.8929 | 1.36003 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −39.3759 | −1.98625 | ||||||||
\(394\) | 27.5040 | 1.38563 | ||||||||
\(395\) | −1.97858 | −0.0995530 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.17935 | 0.259944 | 0.129972 | − | 0.991518i | \(-0.458511\pi\) | ||||
0.129972 | + | 0.991518i | \(0.458511\pi\) | |||||||
\(398\) | 7.56404 | 0.379151 | ||||||||
\(399\) | 1.76060 | 0.0881401 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 32.7434 | 1.63513 | 0.817563 | − | 0.575839i | \(-0.195324\pi\) | ||||
0.817563 | + | 0.575839i | \(0.195324\pi\) | |||||||
\(402\) | −18.8929 | −0.942291 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.48929 | −0.322854 | ||||||||
\(405\) | 8.37169 | 0.415993 | ||||||||
\(406\) | −2.39312 | −0.118768 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 12.9357 | 0.640414 | ||||||||
\(409\) | −17.3717 | −0.858975 | −0.429487 | − | 0.903073i | \(-0.641306\pi\) | ||||
−0.429487 | + | 0.903073i | \(0.641306\pi\) | |||||||
\(410\) | 4.97858 | 0.245874 | ||||||||
\(411\) | 42.6472 | 2.10363 | ||||||||
\(412\) | 3.78202 | 0.186327 | ||||||||
\(413\) | 3.29273 | 0.162025 | ||||||||
\(414\) | 16.5426 | 0.813025 | ||||||||
\(415\) | −4.48929 | −0.220371 | ||||||||
\(416\) | 2.48929 | 0.122047 | ||||||||
\(417\) | 41.0038 | 2.00796 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.31415 | 0.210760 | 0.105380 | − | 0.994432i | \(-0.466394\pi\) | ||||
0.105380 | + | 0.994432i | \(0.466394\pi\) | |||||||
\(420\) | −2.48929 | −0.121465 | ||||||||
\(421\) | −40.7005 | −1.98362 | −0.991811 | − | 0.127711i | \(-0.959237\pi\) | ||||
−0.991811 | + | 0.127711i | \(0.959237\pi\) | |||||||
\(422\) | −20.7862 | −1.01186 | ||||||||
\(423\) | −17.1709 | −0.834879 | ||||||||
\(424\) | −1.19656 | −0.0581100 | ||||||||
\(425\) | 5.19656 | 0.252070 | ||||||||
\(426\) | 30.3074 | 1.46840 | ||||||||
\(427\) | 7.78202 | 0.376598 | ||||||||
\(428\) | −4.21798 | −0.203884 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.15371 | 0.441431 | ||||||||
\(431\) | −31.7862 | −1.53109 | −0.765544 | − | 0.643383i | \(-0.777530\pi\) | ||||
−0.765544 | + | 0.643383i | \(0.777530\pi\) | |||||||
\(432\) | 0.489289 | 0.0235409 | ||||||||
\(433\) | −28.0722 | −1.34907 | −0.674533 | − | 0.738245i | \(-0.735655\pi\) | ||||
−0.674533 | + | 0.738245i | \(0.735655\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.95715 | 0.285624 | ||||||||
\(436\) | −9.37169 | −0.448823 | ||||||||
\(437\) | 3.66021 | 0.175092 | ||||||||
\(438\) | −0.435961 | −0.0208310 | ||||||||
\(439\) | 28.9442 | 1.38143 | 0.690715 | − | 0.723128i | \(-0.257296\pi\) | ||||
0.690715 | + | 0.723128i | \(0.257296\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.19656 | 0.152217 | ||||||||
\(442\) | 12.9357 | 0.615290 | ||||||||
\(443\) | 7.79923 | 0.370553 | 0.185276 | − | 0.982686i | \(-0.440682\pi\) | ||||
0.185276 | + | 0.982686i | \(0.440682\pi\) | |||||||
\(444\) | 18.3503 | 0.870865 | ||||||||
\(445\) | 0.978577 | 0.0463890 | ||||||||
\(446\) | 16.7606 | 0.793637 | ||||||||
\(447\) | −37.1793 | −1.75852 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −11.7862 | −0.556227 | −0.278113 | − | 0.960548i | \(-0.589709\pi\) | ||||
−0.278113 | + | 0.960548i | \(0.589709\pi\) | |||||||
\(450\) | 3.19656 | 0.150687 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 10.5897 | 0.498096 | ||||||||
\(453\) | −32.6901 | −1.53591 | ||||||||
\(454\) | −13.3717 | −0.627565 | ||||||||
\(455\) | −2.48929 | −0.116700 | ||||||||
\(456\) | 1.76060 | 0.0824475 | ||||||||
\(457\) | −30.1109 | −1.40853 | −0.704263 | − | 0.709939i | \(-0.748723\pi\) | ||||
−0.704263 | + | 0.709939i | \(0.748723\pi\) | |||||||
\(458\) | −4.13229 | −0.193089 | ||||||||
\(459\) | 2.54262 | 0.118679 | ||||||||
\(460\) | −5.17513 | −0.241292 | ||||||||
\(461\) | 18.9101 | 0.880731 | 0.440366 | − | 0.897819i | \(-0.354849\pi\) | ||||
0.440366 | + | 0.897819i | \(0.354849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.8543 | −1.24802 | −0.624011 | − | 0.781415i | \(-0.714498\pi\) | ||||
−0.624011 | + | 0.781415i | \(0.714498\pi\) | |||||||
\(464\) | −2.39312 | −0.111098 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.21798 | 0.241718 | ||||||||
\(467\) | −39.9332 | −1.84789 | −0.923944 | − | 0.382527i | \(-0.875054\pi\) | ||||
−0.923944 | + | 0.382527i | \(0.875054\pi\) | |||||||
\(468\) | 7.95715 | 0.367820 | ||||||||
\(469\) | −7.58967 | −0.350459 | ||||||||
\(470\) | 5.37169 | 0.247778 | ||||||||
\(471\) | −22.1109 | −1.01881 | ||||||||
\(472\) | 3.29273 | 0.151560 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4.92525 | 0.226224 | ||||||||
\(475\) | 0.707269 | 0.0324517 | ||||||||
\(476\) | 5.19656 | 0.238184 | ||||||||
\(477\) | −3.82487 | −0.175129 | ||||||||
\(478\) | −30.3032 | −1.38604 | ||||||||
\(479\) | −18.2646 | −0.834530 | −0.417265 | − | 0.908785i | \(-0.637011\pi\) | ||||
−0.417265 | + | 0.908785i | \(0.637011\pi\) | |||||||
\(480\) | −2.48929 | −0.113620 | ||||||||
\(481\) | 18.3503 | 0.836700 | ||||||||
\(482\) | 11.4145 | 0.519918 | ||||||||
\(483\) | 12.8824 | 0.586170 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.17513 | −0.189583 | ||||||||
\(486\) | −22.3074 | −1.01189 | ||||||||
\(487\) | 13.1323 | 0.595081 | 0.297540 | − | 0.954709i | \(-0.403834\pi\) | ||||
0.297540 | + | 0.954709i | \(0.403834\pi\) | |||||||
\(488\) | 7.78202 | 0.352275 | ||||||||
\(489\) | 26.2008 | 1.18484 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −19.4145 | −0.876166 | −0.438083 | − | 0.898935i | \(-0.644342\pi\) | ||||
−0.438083 | + | 0.898935i | \(0.644342\pi\) | |||||||
\(492\) | −12.3931 | −0.558725 | ||||||||
\(493\) | −12.4360 | −0.560088 | ||||||||
\(494\) | 1.76060 | 0.0792130 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.1751 | 0.546129 | ||||||||
\(498\) | 11.1751 | 0.500770 | ||||||||
\(499\) | −10.3503 | −0.463342 | −0.231671 | − | 0.972794i | \(-0.574419\pi\) | ||||
−0.231671 | + | 0.972794i | \(0.574419\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 56.0722 | 2.50512 | ||||||||
\(502\) | −12.7606 | −0.569533 | ||||||||
\(503\) | −22.0894 | −0.984920 | −0.492460 | − | 0.870335i | \(-0.663902\pi\) | ||||
−0.492460 | + | 0.870335i | \(0.663902\pi\) | |||||||
\(504\) | 3.19656 | 0.142386 | ||||||||
\(505\) | 6.48929 | 0.288770 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.9357 | −0.752142 | ||||||||
\(508\) | 2.82487 | 0.125333 | ||||||||
\(509\) | −30.8652 | −1.36808 | −0.684038 | − | 0.729447i | \(-0.739778\pi\) | ||||
−0.684038 | + | 0.729447i | \(0.739778\pi\) | |||||||
\(510\) | −12.9357 | −0.572804 | ||||||||
\(511\) | −0.175135 | −0.00774750 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.346059 | 0.0152789 | ||||||||
\(514\) | −3.58967 | −0.158334 | ||||||||
\(515\) | −3.78202 | −0.166656 | ||||||||
\(516\) | −22.7862 | −1.00311 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 7.37169 | 0.323894 | ||||||||
\(519\) | −33.7648 | −1.48211 | ||||||||
\(520\) | −2.48929 | −0.109163 | ||||||||
\(521\) | −0.350269 | −0.0153456 | −0.00767279 | − | 0.999971i | \(-0.502442\pi\) | ||||
−0.00767279 | + | 0.999971i | \(0.502442\pi\) | |||||||
\(522\) | −7.64973 | −0.334820 | ||||||||
\(523\) | 25.1898 | 1.10147 | 0.550737 | − | 0.834679i | \(-0.314347\pi\) | ||||
0.550737 | + | 0.834679i | \(0.314347\pi\) | |||||||
\(524\) | −15.8181 | −0.691018 | ||||||||
\(525\) | 2.48929 | 0.108641 | ||||||||
\(526\) | 2.63252 | 0.114783 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.78202 | 0.164436 | ||||||||
\(530\) | 1.19656 | 0.0519751 | ||||||||
\(531\) | 10.5254 | 0.456764 | ||||||||
\(532\) | 0.707269 | 0.0306640 | ||||||||
\(533\) | −12.3931 | −0.536805 | ||||||||
\(534\) | −2.43596 | −0.105414 | ||||||||
\(535\) | 4.21798 | 0.182359 | ||||||||
\(536\) | −7.58967 | −0.327824 | ||||||||
\(537\) | 65.5934 | 2.83057 | ||||||||
\(538\) | 12.8996 | 0.556142 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.489289 | −0.0210556 | ||||||||
\(541\) | 0.243614 | 0.0104738 | 0.00523689 | − | 0.999986i | \(-0.498333\pi\) | ||||
0.00523689 | + | 0.999986i | \(0.498333\pi\) | |||||||
\(542\) | −8.93573 | −0.383823 | ||||||||
\(543\) | 3.69679 | 0.158644 | ||||||||
\(544\) | 5.19656 | 0.222801 | ||||||||
\(545\) | 9.37169 | 0.401439 | ||||||||
\(546\) | 6.19656 | 0.265188 | ||||||||
\(547\) | 28.4826 | 1.21783 | 0.608913 | − | 0.793237i | \(-0.291606\pi\) | ||||
0.608913 | + | 0.793237i | \(0.291606\pi\) | |||||||
\(548\) | 17.1323 | 0.731855 | ||||||||
\(549\) | 24.8757 | 1.06167 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.69258 | −0.0721062 | ||||||||
\(552\) | 12.8824 | 0.548312 | ||||||||
\(553\) | 1.97858 | 0.0841377 | ||||||||
\(554\) | −10.0000 | −0.424859 | ||||||||
\(555\) | −18.3503 | −0.778926 | ||||||||
\(556\) | 16.4721 | 0.698572 | ||||||||
\(557\) | −18.3931 | −0.779341 | −0.389671 | − | 0.920954i | \(-0.627411\pi\) | ||||
−0.389671 | + | 0.920954i | \(0.627411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.7862 | −0.963755 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.5212 | 0.865634 | ||||||||
\(563\) | −20.4464 | −0.861715 | −0.430857 | − | 0.902420i | \(-0.641789\pi\) | ||||
−0.430857 | + | 0.902420i | \(0.641789\pi\) | |||||||
\(564\) | −13.3717 | −0.563050 | ||||||||
\(565\) | −10.5897 | −0.445511 | ||||||||
\(566\) | −0.681635 | −0.0286513 | ||||||||
\(567\) | −8.37169 | −0.351578 | ||||||||
\(568\) | 12.1751 | 0.510857 | ||||||||
\(569\) | −7.67115 | −0.321591 | −0.160796 | − | 0.986988i | \(-0.551406\pi\) | ||||
−0.160796 | + | 0.986988i | \(0.551406\pi\) | |||||||
\(570\) | −1.76060 | −0.0737433 | ||||||||
\(571\) | −0.149501 | −0.00625642 | −0.00312821 | − | 0.999995i | \(-0.500996\pi\) | ||||
−0.00312821 | + | 0.999995i | \(0.500996\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.3822 | 1.06036 | ||||||||
\(574\) | −4.97858 | −0.207802 | ||||||||
\(575\) | 5.17513 | 0.215818 | ||||||||
\(576\) | 3.19656 | 0.133190 | ||||||||
\(577\) | 14.0256 | 0.583895 | 0.291947 | − | 0.956434i | \(-0.405697\pi\) | ||||
0.291947 | + | 0.956434i | \(0.405697\pi\) | |||||||
\(578\) | 10.0042 | 0.416120 | ||||||||
\(579\) | −27.3393 | −1.13618 | ||||||||
\(580\) | 2.39312 | 0.0993687 | ||||||||
\(581\) | 4.48929 | 0.186247 | ||||||||
\(582\) | 10.3931 | 0.430808 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.175135 | −0.00724713 | ||||||||
\(585\) | −7.95715 | −0.328988 | ||||||||
\(586\) | −19.4250 | −0.802440 | ||||||||
\(587\) | 28.8396 | 1.19034 | 0.595168 | − | 0.803601i | \(-0.297086\pi\) | ||||
0.595168 | + | 0.803601i | \(0.297086\pi\) | |||||||
\(588\) | 2.48929 | 0.102657 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −3.29273 | −0.135560 | ||||||||
\(591\) | 68.4653 | 2.81629 | ||||||||
\(592\) | 7.37169 | 0.302975 | ||||||||
\(593\) | 22.9529 | 0.942564 | 0.471282 | − | 0.881982i | \(-0.343791\pi\) | ||||
0.471282 | + | 0.881982i | \(0.343791\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.19656 | −0.213038 | ||||||||
\(596\) | −14.9357 | −0.611791 | ||||||||
\(597\) | 18.8291 | 0.770623 | ||||||||
\(598\) | 12.8824 | 0.526801 | ||||||||
\(599\) | −0.807653 | −0.0329998 | −0.0164999 | − | 0.999864i | \(-0.505252\pi\) | ||||
−0.0164999 | + | 0.999864i | \(0.505252\pi\) | |||||||
\(600\) | 2.48929 | 0.101625 | ||||||||
\(601\) | −7.21377 | −0.294256 | −0.147128 | − | 0.989117i | \(-0.547003\pi\) | ||||
−0.147128 | + | 0.989117i | \(0.547003\pi\) | |||||||
\(602\) | −9.15371 | −0.373077 | ||||||||
\(603\) | −24.2608 | −0.987977 | ||||||||
\(604\) | −13.1323 | −0.534345 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.1537 | −0.656200 | ||||||||
\(607\) | 2.52540 | 0.102503 | 0.0512515 | − | 0.998686i | \(-0.483679\pi\) | ||||
0.0512515 | + | 0.998686i | \(0.483679\pi\) | |||||||
\(608\) | 0.707269 | 0.0286835 | ||||||||
\(609\) | −5.95715 | −0.241396 | ||||||||
\(610\) | −7.78202 | −0.315085 | ||||||||
\(611\) | −13.3717 | −0.540961 | ||||||||
\(612\) | 16.6111 | 0.671464 | ||||||||
\(613\) | 3.19656 | 0.129108 | 0.0645539 | − | 0.997914i | \(-0.479438\pi\) | ||||
0.0645539 | + | 0.997914i | \(0.479438\pi\) | |||||||
\(614\) | 14.1923 | 0.572757 | ||||||||
\(615\) | 12.3931 | 0.499739 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.6577 | −1.47578 | −0.737892 | − | 0.674919i | \(-0.764178\pi\) | ||||
−0.737892 | + | 0.674919i | \(0.764178\pi\) | |||||||
\(618\) | 9.41454 | 0.378708 | ||||||||
\(619\) | −35.6174 | −1.43158 | −0.715791 | − | 0.698314i | \(-0.753934\pi\) | ||||
−0.715791 | + | 0.698314i | \(0.753934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.53213 | 0.101611 | ||||||||
\(622\) | −28.8929 | −1.15850 | ||||||||
\(623\) | −0.978577 | −0.0392059 | ||||||||
\(624\) | 6.19656 | 0.248061 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.0000 | −0.399680 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.88240 | −0.354446 | ||||||||
\(629\) | 38.3074 | 1.52742 | ||||||||
\(630\) | −3.19656 | −0.127354 | ||||||||
\(631\) | −35.6535 | −1.41934 | −0.709671 | − | 0.704533i | \(-0.751157\pi\) | ||||
−0.709671 | + | 0.704533i | \(0.751157\pi\) | |||||||
\(632\) | 1.97858 | 0.0787036 | ||||||||
\(633\) | −51.7429 | −2.05660 | ||||||||
\(634\) | 7.97437 | 0.316703 | ||||||||
\(635\) | −2.82487 | −0.112101 | ||||||||
\(636\) | −2.97858 | −0.118108 | ||||||||
\(637\) | 2.48929 | 0.0986292 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 38.9185 | 1.53959 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 5.97858 | 0.236140 | 0.118070 | − | 0.993005i | \(-0.462329\pi\) | ||||
0.118070 | + | 0.993005i | \(0.462329\pi\) | |||||||
\(642\) | −10.4998 | −0.414393 | ||||||||
\(643\) | −41.3717 | −1.63154 | −0.815770 | − | 0.578376i | \(-0.803687\pi\) | ||||
−0.815770 | + | 0.578376i | \(0.803687\pi\) | |||||||
\(644\) | 5.17513 | 0.203929 | ||||||||
\(645\) | 22.7862 | 0.897207 | ||||||||
\(646\) | 3.67536 | 0.144605 | ||||||||
\(647\) | 42.2902 | 1.66260 | 0.831300 | − | 0.555824i | \(-0.187597\pi\) | ||||
0.831300 | + | 0.555824i | \(0.187597\pi\) | |||||||
\(648\) | −8.37169 | −0.328871 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.48929 | 0.0976379 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.5254 | 0.412207 | ||||||||
\(653\) | 18.7262 | 0.732812 | 0.366406 | − | 0.930455i | \(-0.380588\pi\) | ||||
0.366406 | + | 0.930455i | \(0.380588\pi\) | |||||||
\(654\) | −23.3288 | −0.912230 | ||||||||
\(655\) | 15.8181 | 0.618066 | ||||||||
\(656\) | −4.97858 | −0.194381 | ||||||||
\(657\) | −0.559828 | −0.0218410 | ||||||||
\(658\) | −5.37169 | −0.209410 | ||||||||
\(659\) | −23.9143 | −0.931569 | −0.465785 | − | 0.884898i | \(-0.654228\pi\) | ||||
−0.465785 | + | 0.884898i | \(0.654228\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.6174 | 1.61873 | 0.809364 | − | 0.587307i | \(-0.199812\pi\) | ||||
0.809364 | + | 0.587307i | \(0.199812\pi\) | |||||||
\(662\) | 8.62831 | 0.335349 | ||||||||
\(663\) | 32.2008 | 1.25057 | ||||||||
\(664\) | 4.48929 | 0.174218 | ||||||||
\(665\) | −0.707269 | −0.0274267 | ||||||||
\(666\) | 23.5640 | 0.913088 | ||||||||
\(667\) | −12.3847 | −0.479537 | ||||||||
\(668\) | 22.5254 | 0.871534 | ||||||||
\(669\) | 41.7220 | 1.61306 | ||||||||
\(670\) | 7.58967 | 0.293215 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.48929 | 0.0960264 | ||||||||
\(673\) | 25.5254 | 0.983932 | 0.491966 | − | 0.870614i | \(-0.336278\pi\) | ||||
0.491966 | + | 0.870614i | \(0.336278\pi\) | |||||||
\(674\) | −7.80344 | −0.300577 | ||||||||
\(675\) | 0.489289 | 0.0188327 | ||||||||
\(676\) | −6.80344 | −0.261671 | ||||||||
\(677\) | −21.8610 | −0.840186 | −0.420093 | − | 0.907481i | \(-0.638003\pi\) | ||||
−0.420093 | + | 0.907481i | \(0.638003\pi\) | |||||||
\(678\) | 26.3608 | 1.01238 | ||||||||
\(679\) | 4.17513 | 0.160227 | ||||||||
\(680\) | −5.19656 | −0.199279 | ||||||||
\(681\) | −33.2860 | −1.27552 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.9744 | −0.458186 | −0.229093 | − | 0.973404i | \(-0.573576\pi\) | ||||
−0.229093 | + | 0.973404i | \(0.573576\pi\) | |||||||
\(684\) | 2.26083 | 0.0864448 | ||||||||
\(685\) | −17.1323 | −0.654591 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −10.2865 | −0.392453 | ||||||||
\(688\) | −9.15371 | −0.348982 | ||||||||
\(689\) | −2.97858 | −0.113475 | ||||||||
\(690\) | −12.8824 | −0.490425 | ||||||||
\(691\) | −29.4611 | −1.12075 | −0.560377 | − | 0.828238i | \(-0.689344\pi\) | ||||
−0.560377 | + | 0.828238i | \(0.689344\pi\) | |||||||
\(692\) | −13.5640 | −0.515627 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.1966 | 1.03237 | ||||||||
\(695\) | −16.4721 | −0.624821 | ||||||||
\(696\) | −5.95715 | −0.225805 | ||||||||
\(697\) | −25.8715 | −0.979952 | ||||||||
\(698\) | −28.0533 | −1.06183 | ||||||||
\(699\) | 12.9891 | 0.491291 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 8.58546 | 0.324268 | 0.162134 | − | 0.986769i | \(-0.448162\pi\) | ||||
0.162134 | + | 0.986769i | \(0.448162\pi\) | |||||||
\(702\) | 1.21798 | 0.0459697 | ||||||||
\(703\) | 5.21377 | 0.196641 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.3717 | 0.503607 | ||||||||
\(706\) | 12.5254 | 0.471400 | ||||||||
\(707\) | −6.48929 | −0.244055 | ||||||||
\(708\) | 8.19656 | 0.308045 | ||||||||
\(709\) | −18.7005 | −0.702313 | −0.351157 | − | 0.936317i | \(-0.614212\pi\) | ||||
−0.351157 | + | 0.936317i | \(0.614212\pi\) | |||||||
\(710\) | −12.1751 | −0.456925 | ||||||||
\(711\) | 6.32464 | 0.237192 | ||||||||
\(712\) | −0.978577 | −0.0366737 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 12.9357 | 0.484108 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.3503 | 0.984756 | ||||||||
\(717\) | −75.4334 | −2.81711 | ||||||||
\(718\) | −21.3461 | −0.796628 | ||||||||
\(719\) | −17.1365 | −0.639084 | −0.319542 | − | 0.947572i | \(-0.603529\pi\) | ||||
−0.319542 | + | 0.947572i | \(0.603529\pi\) | |||||||
\(720\) | −3.19656 | −0.119129 | ||||||||
\(721\) | 3.78202 | 0.140850 | ||||||||
\(722\) | −18.4998 | −0.688490 | ||||||||
\(723\) | 28.4141 | 1.05673 | ||||||||
\(724\) | 1.48508 | 0.0551925 | ||||||||
\(725\) | −2.39312 | −0.0888781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.41454 | 0.274990 | 0.137495 | − | 0.990502i | \(-0.456095\pi\) | ||||
0.137495 | + | 0.990502i | \(0.456095\pi\) | |||||||
\(728\) | 2.48929 | 0.0922592 | ||||||||
\(729\) | −30.4145 | −1.12646 | ||||||||
\(730\) | 0.175135 | 0.00648203 | ||||||||
\(731\) | −47.5678 | −1.75936 | ||||||||
\(732\) | 19.3717 | 0.715998 | ||||||||
\(733\) | −38.9546 | −1.43882 | −0.719411 | − | 0.694584i | \(-0.755588\pi\) | ||||
−0.719411 | + | 0.694584i | \(0.755588\pi\) | |||||||
\(734\) | 24.7178 | 0.912349 | ||||||||
\(735\) | −2.48929 | −0.0918188 | ||||||||
\(736\) | 5.17513 | 0.190758 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −15.9143 | −0.585814 | ||||||||
\(739\) | −1.84208 | −0.0677619 | −0.0338810 | − | 0.999426i | \(-0.510787\pi\) | ||||
−0.0338810 | + | 0.999426i | \(0.510787\pi\) | |||||||
\(740\) | −7.37169 | −0.270989 | ||||||||
\(741\) | 4.38263 | 0.161000 | ||||||||
\(742\) | −1.19656 | −0.0439270 | ||||||||
\(743\) | 7.56404 | 0.277498 | 0.138749 | − | 0.990328i | \(-0.455692\pi\) | ||||
0.138749 | + | 0.990328i | \(0.455692\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.9357 | 0.547203 | ||||||||
\(746\) | −12.9185 | −0.472981 | ||||||||
\(747\) | 14.3503 | 0.525049 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.21798 | −0.154122 | ||||||||
\(750\) | −2.48929 | −0.0908960 | ||||||||
\(751\) | −11.9614 | −0.436476 | −0.218238 | − | 0.975896i | \(-0.570031\pi\) | ||||
−0.218238 | + | 0.975896i | \(0.570031\pi\) | |||||||
\(752\) | −5.37169 | −0.195885 | ||||||||
\(753\) | −31.7648 | −1.15757 | ||||||||
\(754\) | −5.95715 | −0.216947 | ||||||||
\(755\) | 13.1323 | 0.477933 | ||||||||
\(756\) | 0.489289 | 0.0177953 | ||||||||
\(757\) | −35.1966 | −1.27924 | −0.639620 | − | 0.768691i | \(-0.720908\pi\) | ||||
−0.639620 | + | 0.768691i | \(0.720908\pi\) | |||||||
\(758\) | 35.9227 | 1.30477 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.707269 | −0.0256553 | ||||||||
\(761\) | 27.3288 | 0.990670 | 0.495335 | − | 0.868702i | \(-0.335045\pi\) | ||||
0.495335 | + | 0.868702i | \(0.335045\pi\) | |||||||
\(762\) | 7.03190 | 0.254739 | ||||||||
\(763\) | −9.37169 | −0.339278 | ||||||||
\(764\) | 10.1966 | 0.368899 | ||||||||
\(765\) | −16.6111 | −0.600575 | ||||||||
\(766\) | 11.6325 | 0.420300 | ||||||||
\(767\) | 8.19656 | 0.295961 | ||||||||
\(768\) | 2.48929 | 0.0898245 | ||||||||
\(769\) | 43.2860 | 1.56093 | 0.780467 | − | 0.625198i | \(-0.214982\pi\) | ||||
0.780467 | + | 0.625198i | \(0.214982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.93573 | −0.321813 | ||||||||
\(772\) | −10.9828 | −0.395279 | ||||||||
\(773\) | −39.7324 | −1.42908 | −0.714538 | − | 0.699596i | \(-0.753363\pi\) | ||||
−0.714538 | + | 0.699596i | \(0.753363\pi\) | |||||||
\(774\) | −29.2604 | −1.05174 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.17513 | 0.149879 | ||||||||
\(777\) | 18.3503 | 0.658312 | ||||||||
\(778\) | −25.2860 | −0.906547 | ||||||||
\(779\) | −3.52119 | −0.126160 | ||||||||
\(780\) | −6.19656 | −0.221872 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 26.8929 | 0.961688 | ||||||||
\(783\) | −1.17092 | −0.0418454 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 8.88240 | 0.317027 | ||||||||
\(786\) | −39.3759 | −1.40449 | ||||||||
\(787\) | −2.97858 | −0.106175 | −0.0530874 | − | 0.998590i | \(-0.516906\pi\) | ||||
−0.0530874 | + | 0.998590i | \(0.516906\pi\) | |||||||
\(788\) | 27.5040 | 0.979789 | ||||||||
\(789\) | 6.55310 | 0.233296 | ||||||||
\(790\) | −1.97858 | −0.0703946 | ||||||||
\(791\) | 10.5897 | 0.376525 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.3717 | 0.687909 | ||||||||
\(794\) | 5.17935 | 0.183808 | ||||||||
\(795\) | 2.97858 | 0.105639 | ||||||||
\(796\) | 7.56404 | 0.268100 | ||||||||
\(797\) | 33.6258 | 1.19109 | 0.595543 | − | 0.803323i | \(-0.296937\pi\) | ||||
0.595543 | + | 0.803323i | \(0.296937\pi\) | |||||||
\(798\) | 1.76060 | 0.0623244 | ||||||||
\(799\) | −27.9143 | −0.987537 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −3.12808 | −0.110525 | ||||||||
\(802\) | 32.7434 | 1.15621 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −18.8929 | −0.666301 | ||||||||
\(805\) | −5.17513 | −0.182400 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.1109 | 1.13036 | ||||||||
\(808\) | −6.48929 | −0.228292 | ||||||||
\(809\) | 29.3545 | 1.03205 | 0.516024 | − | 0.856574i | \(-0.327411\pi\) | ||||
0.516024 | + | 0.856574i | \(0.327411\pi\) | |||||||
\(810\) | 8.37169 | 0.294151 | ||||||||
\(811\) | −28.9013 | −1.01486 | −0.507431 | − | 0.861692i | \(-0.669405\pi\) | ||||
−0.507431 | + | 0.861692i | \(0.669405\pi\) | |||||||
\(812\) | −2.39312 | −0.0839819 | ||||||||
\(813\) | −22.2436 | −0.780118 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.5254 | −0.368689 | ||||||||
\(816\) | 12.9357 | 0.452841 | ||||||||
\(817\) | −6.47414 | −0.226501 | ||||||||
\(818\) | −17.3717 | −0.607387 | ||||||||
\(819\) | 7.95715 | 0.278045 | ||||||||
\(820\) | 4.97858 | 0.173859 | ||||||||
\(821\) | −42.1495 | −1.47103 | −0.735514 | − | 0.677510i | \(-0.763059\pi\) | ||||
−0.735514 | + | 0.677510i | \(0.763059\pi\) | |||||||
\(822\) | 42.6472 | 1.48749 | ||||||||
\(823\) | −42.3931 | −1.47773 | −0.738866 | − | 0.673853i | \(-0.764638\pi\) | ||||
−0.738866 | + | 0.673853i | \(0.764638\pi\) | |||||||
\(824\) | 3.78202 | 0.131753 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.29273 | 0.114569 | ||||||||
\(827\) | 54.3969 | 1.89156 | 0.945782 | − | 0.324802i | \(-0.105298\pi\) | ||||
0.945782 | + | 0.324802i | \(0.105298\pi\) | |||||||
\(828\) | 16.5426 | 0.574896 | ||||||||
\(829\) | 29.6174 | 1.02865 | 0.514327 | − | 0.857594i | \(-0.328042\pi\) | ||||
0.514327 | + | 0.857594i | \(0.328042\pi\) | |||||||
\(830\) | −4.48929 | −0.155825 | ||||||||
\(831\) | −24.8929 | −0.863525 | ||||||||
\(832\) | 2.48929 | 0.0863006 | ||||||||
\(833\) | 5.19656 | 0.180050 | ||||||||
\(834\) | 41.0038 | 1.41984 | ||||||||
\(835\) | −22.5254 | −0.779524 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.31415 | 0.149030 | ||||||||
\(839\) | 46.4998 | 1.60535 | 0.802675 | − | 0.596416i | \(-0.203409\pi\) | ||||
0.802675 | + | 0.596416i | \(0.203409\pi\) | |||||||
\(840\) | −2.48929 | −0.0858886 | ||||||||
\(841\) | −23.2730 | −0.802517 | ||||||||
\(842\) | −40.7005 | −1.40263 | ||||||||
\(843\) | 51.0832 | 1.75940 | ||||||||
\(844\) | −20.7862 | −0.715492 | ||||||||
\(845\) | 6.80344 | 0.234046 | ||||||||
\(846\) | −17.1709 | −0.590349 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.19656 | −0.0410900 | ||||||||
\(849\) | −1.69679 | −0.0582336 | ||||||||
\(850\) | 5.19656 | 0.178240 | ||||||||
\(851\) | 38.1495 | 1.30775 | ||||||||
\(852\) | 30.3074 | 1.03832 | ||||||||
\(853\) | −23.5536 | −0.806458 | −0.403229 | − | 0.915099i | \(-0.632112\pi\) | ||||
−0.403229 | + | 0.915099i | \(0.632112\pi\) | |||||||
\(854\) | 7.78202 | 0.266295 | ||||||||
\(855\) | −2.26083 | −0.0773186 | ||||||||
\(856\) | −4.21798 | −0.144168 | ||||||||
\(857\) | 18.9786 | 0.648296 | 0.324148 | − | 0.946006i | \(-0.394922\pi\) | ||||
0.324148 | + | 0.946006i | \(0.394922\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.3246 | −0.556989 | −0.278495 | − | 0.960438i | \(-0.589835\pi\) | ||||
−0.278495 | + | 0.960438i | \(0.589835\pi\) | |||||||
\(860\) | 9.15371 | 0.312139 | ||||||||
\(861\) | −12.3931 | −0.422356 | ||||||||
\(862\) | −31.7862 | −1.08264 | ||||||||
\(863\) | −38.3074 | −1.30400 | −0.652000 | − | 0.758219i | \(-0.726070\pi\) | ||||
−0.652000 | + | 0.758219i | \(0.726070\pi\) | |||||||
\(864\) | 0.489289 | 0.0166459 | ||||||||
\(865\) | 13.5640 | 0.461191 | ||||||||
\(866\) | −28.0722 | −0.953933 | ||||||||
\(867\) | 24.9034 | 0.845763 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 5.95715 | 0.201966 | ||||||||
\(871\) | −18.8929 | −0.640161 | ||||||||
\(872\) | −9.37169 | −0.317366 | ||||||||
\(873\) | 13.3461 | 0.451696 | ||||||||
\(874\) | 3.66021 | 0.123809 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −0.435961 | −0.0147298 | ||||||||
\(877\) | −20.4826 | −0.691647 | −0.345823 | − | 0.938300i | \(-0.612400\pi\) | ||||
−0.345823 | + | 0.938300i | \(0.612400\pi\) | |||||||
\(878\) | 28.9442 | 0.976818 | ||||||||
\(879\) | −48.3545 | −1.63096 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.0937 | −0.441136 | −0.220568 | − | 0.975372i | \(-0.570791\pi\) | ||||
−0.220568 | + | 0.975372i | \(0.570791\pi\) | |||||||
\(882\) | 3.19656 | 0.107634 | ||||||||
\(883\) | 21.1537 | 0.711879 | 0.355940 | − | 0.934509i | \(-0.384161\pi\) | ||||
0.355940 | + | 0.934509i | \(0.384161\pi\) | |||||||
\(884\) | 12.9357 | 0.435076 | ||||||||
\(885\) | −8.19656 | −0.275524 | ||||||||
\(886\) | 7.79923 | 0.262020 | ||||||||
\(887\) | −14.7350 | −0.494752 | −0.247376 | − | 0.968920i | \(-0.579568\pi\) | ||||
−0.247376 | + | 0.968920i | \(0.579568\pi\) | |||||||
\(888\) | 18.3503 | 0.615795 | ||||||||
\(889\) | 2.82487 | 0.0947429 | ||||||||
\(890\) | 0.978577 | 0.0328020 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.7606 | 0.561186 | ||||||||
\(893\) | −3.79923 | −0.127136 | ||||||||
\(894\) | −37.1793 | −1.24346 | ||||||||
\(895\) | −26.3503 | −0.880792 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 32.0680 | 1.07072 | ||||||||
\(898\) | −11.7862 | −0.393312 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 3.19656 | 0.106552 | ||||||||
\(901\) | −6.21798 | −0.207151 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −22.7862 | −0.758278 | ||||||||
\(904\) | 10.5897 | 0.352207 | ||||||||
\(905\) | −1.48508 | −0.0493657 | ||||||||
\(906\) | −32.6901 | −1.08605 | ||||||||
\(907\) | −27.3032 | −0.906588 | −0.453294 | − | 0.891361i | \(-0.649751\pi\) | ||||
−0.453294 | + | 0.891361i | \(0.649751\pi\) | |||||||
\(908\) | −13.3717 | −0.443755 | ||||||||
\(909\) | −20.7434 | −0.688015 | ||||||||
\(910\) | −2.48929 | −0.0825191 | ||||||||
\(911\) | −26.1709 | −0.867081 | −0.433541 | − | 0.901134i | \(-0.642736\pi\) | ||||
−0.433541 | + | 0.901134i | \(0.642736\pi\) | |||||||
\(912\) | 1.76060 | 0.0582992 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −30.1109 | −0.995979 | ||||||||
\(915\) | −19.3717 | −0.640408 | ||||||||
\(916\) | −4.13229 | −0.136535 | ||||||||
\(917\) | −15.8181 | −0.522361 | ||||||||
\(918\) | 2.54262 | 0.0839188 | ||||||||
\(919\) | −39.1281 | −1.29072 | −0.645358 | − | 0.763880i | \(-0.723292\pi\) | ||||
−0.645358 | + | 0.763880i | \(0.723292\pi\) | |||||||
\(920\) | −5.17513 | −0.170619 | ||||||||
\(921\) | 35.3288 | 1.16413 | ||||||||
\(922\) | 18.9101 | 0.622771 | ||||||||
\(923\) | 30.3074 | 0.997581 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.37169 | 0.242380 | ||||||||
\(926\) | −26.8543 | −0.882485 | ||||||||
\(927\) | 12.0894 | 0.397069 | ||||||||
\(928\) | −2.39312 | −0.0785579 | ||||||||
\(929\) | 60.2302 | 1.97609 | 0.988044 | − | 0.154175i | \(-0.0492718\pi\) | ||||
0.988044 | + | 0.154175i | \(0.0492718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.707269 | 0.0231798 | ||||||||
\(932\) | 5.21798 | 0.170921 | ||||||||
\(933\) | −71.9227 | −2.35464 | ||||||||
\(934\) | −39.9332 | −1.30665 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.95715 | 0.260088 | ||||||||
\(937\) | 3.36327 | 0.109873 | 0.0549366 | − | 0.998490i | \(-0.482504\pi\) | ||||
0.0549366 | + | 0.998490i | \(0.482504\pi\) | |||||||
\(938\) | −7.58967 | −0.247812 | ||||||||
\(939\) | −24.8929 | −0.812349 | ||||||||
\(940\) | 5.37169 | 0.175205 | ||||||||
\(941\) | −6.22640 | −0.202975 | −0.101487 | − | 0.994837i | \(-0.532360\pi\) | ||||
−0.101487 | + | 0.994837i | \(0.532360\pi\) | |||||||
\(942\) | −22.1109 | −0.720411 | ||||||||
\(943\) | −25.7648 | −0.839018 | ||||||||
\(944\) | 3.29273 | 0.107169 | ||||||||
\(945\) | −0.489289 | −0.0159166 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.2432 | −0.755301 | −0.377651 | − | 0.925948i | \(-0.623268\pi\) | ||||
−0.377651 | + | 0.925948i | \(0.623268\pi\) | |||||||
\(948\) | 4.92525 | 0.159965 | ||||||||
\(949\) | −0.435961 | −0.0141519 | ||||||||
\(950\) | 0.707269 | 0.0229468 | ||||||||
\(951\) | 19.8505 | 0.643697 | ||||||||
\(952\) | 5.19656 | 0.168421 | ||||||||
\(953\) | −9.87567 | −0.319904 | −0.159952 | − | 0.987125i | \(-0.551134\pi\) | ||||
−0.159952 | + | 0.987125i | \(0.551134\pi\) | |||||||
\(954\) | −3.82487 | −0.123835 | ||||||||
\(955\) | −10.1966 | −0.329953 | ||||||||
\(956\) | −30.3032 | −0.980076 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.2646 | −0.590102 | ||||||||
\(959\) | 17.1323 | 0.553230 | ||||||||
\(960\) | −2.48929 | −0.0803414 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 18.3503 | 0.591636 | ||||||||
\(963\) | −13.4830 | −0.434484 | ||||||||
\(964\) | 11.4145 | 0.367638 | ||||||||
\(965\) | 10.9828 | 0.353548 | ||||||||
\(966\) | 12.8824 | 0.414485 | ||||||||
\(967\) | −37.1365 | −1.19423 | −0.597115 | − | 0.802156i | \(-0.703686\pi\) | ||||
−0.597115 | + | 0.802156i | \(0.703686\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.14904 | 0.293910 | ||||||||
\(970\) | −4.17513 | −0.134055 | ||||||||
\(971\) | 28.8223 | 0.924953 | 0.462477 | − | 0.886632i | \(-0.346961\pi\) | ||||
0.462477 | + | 0.886632i | \(0.346961\pi\) | |||||||
\(972\) | −22.3074 | −0.715511 | ||||||||
\(973\) | 16.4721 | 0.528071 | ||||||||
\(974\) | 13.1323 | 0.420786 | ||||||||
\(975\) | 6.19656 | 0.198449 | ||||||||
\(976\) | 7.78202 | 0.249096 | ||||||||
\(977\) | 43.6111 | 1.39524 | 0.697621 | − | 0.716467i | \(-0.254242\pi\) | ||||
0.697621 | + | 0.716467i | \(0.254242\pi\) | |||||||
\(978\) | 26.2008 | 0.837808 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −29.9572 | −0.956458 | ||||||||
\(982\) | −19.4145 | −0.619543 | ||||||||
\(983\) | 12.1923 | 0.388875 | 0.194438 | − | 0.980915i | \(-0.437712\pi\) | ||||
0.194438 | + | 0.980915i | \(0.437712\pi\) | |||||||
\(984\) | −12.3931 | −0.395078 | ||||||||
\(985\) | −27.5040 | −0.876350 | ||||||||
\(986\) | −12.4360 | −0.396042 | ||||||||
\(987\) | −13.3717 | −0.425626 | ||||||||
\(988\) | 1.76060 | 0.0560120 | ||||||||
\(989\) | −47.3717 | −1.50633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.3717 | 0.710660 | 0.355330 | − | 0.934741i | \(-0.384368\pi\) | ||||
0.355330 | + | 0.934741i | \(0.384368\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.4783 | 0.681595 | ||||||||
\(994\) | 12.1751 | 0.386172 | ||||||||
\(995\) | −7.56404 | −0.239796 | ||||||||
\(996\) | 11.1751 | 0.354098 | ||||||||
\(997\) | 32.4036 | 1.02623 | 0.513116 | − | 0.858319i | \(-0.328491\pi\) | ||||
0.513116 | + | 0.858319i | \(0.328491\pi\) | |||||||
\(998\) | −10.3503 | −0.327632 | ||||||||
\(999\) | 3.60688 | 0.114117 |
(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 | 8470.2.a.ck.1.3 | yes | 3 | |
11.10 | odd | 2 | 8470.2.a.cg.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.cg.1.3 | ✓ | 3 | 11.10 | odd | 2 | ||
8470.2.a.ck.1.3 | yes | 3 | 1.1 | even | 1 | trivial |