Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2310,2,Mod(1,2310)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2310, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2310.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2310.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: | \(18.4454428669\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2310.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.46410 | 0.960769 | 0.480384 | − | 0.877058i | \(-0.340497\pi\) | ||||
0.480384 | + | 0.877058i | \(0.340497\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −1.46410 | −0.305286 | −0.152643 | − | 0.988281i | \(-0.548779\pi\) | ||||
−0.152643 | + | 0.988281i | \(0.548779\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.46410 | 0.679366 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 6.92820 | 1.24434 | 0.622171 | − | 0.782881i | \(-0.286251\pi\) | ||||
0.622171 | + | 0.782881i | \(0.286251\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −3.46410 | −0.594089 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.46410 | 1.22709 | 0.613545 | − | 0.789659i | \(-0.289743\pi\) | ||||
0.613545 | + | 0.789659i | \(0.289743\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.46410 | −0.554700 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −8.92820 | −1.39435 | −0.697176 | − | 0.716900i | \(-0.745560\pi\) | ||||
−0.697176 | + | 0.716900i | \(0.745560\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −2.92820 | −0.446547 | −0.223273 | − | 0.974756i | \(-0.571674\pi\) | ||||
−0.223273 | + | 0.974756i | \(0.571674\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −1.46410 | −0.215870 | ||||||||
\(47\) | 6.92820 | 1.01058 | 0.505291 | − | 0.862949i | \(-0.331385\pi\) | ||||
0.505291 | + | 0.862949i | \(0.331385\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 3.46410 | 0.485071 | ||||||||
\(52\) | 3.46410 | 0.480384 | ||||||||
\(53\) | 12.9282 | 1.77583 | 0.887913 | − | 0.460012i | \(-0.152155\pi\) | ||||
0.887913 | + | 0.460012i | \(0.152155\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | −2.92820 | −0.381220 | −0.190610 | − | 0.981666i | \(-0.561047\pi\) | ||||
−0.190610 | + | 0.981666i | \(0.561047\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −4.92820 | −0.630992 | −0.315496 | − | 0.948927i | \(-0.602171\pi\) | ||||
−0.315496 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(62\) | 6.92820 | 0.879883 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 9.46410 | 1.15622 | 0.578112 | − | 0.815957i | \(-0.303790\pi\) | ||||
0.578112 | + | 0.815957i | \(0.303790\pi\) | |||||||
\(68\) | −3.46410 | −0.420084 | ||||||||
\(69\) | 1.46410 | 0.176257 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −0.928203 | −0.108638 | −0.0543190 | − | 0.998524i | \(-0.517299\pi\) | ||||
−0.0543190 | + | 0.998524i | \(0.517299\pi\) | |||||||
\(74\) | 7.46410 | 0.867684 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | −3.46410 | −0.392232 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.92820 | −0.985955 | ||||||||
\(83\) | 6.92820 | 0.760469 | 0.380235 | − | 0.924890i | \(-0.375843\pi\) | ||||
0.380235 | + | 0.924890i | \(0.375843\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 3.46410 | 0.375735 | ||||||||
\(86\) | −2.92820 | −0.315756 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 3.46410 | 0.367194 | 0.183597 | − | 0.983002i | \(-0.441226\pi\) | ||||
0.183597 | + | 0.983002i | \(0.441226\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 3.46410 | 0.363137 | ||||||||
\(92\) | −1.46410 | −0.152643 | ||||||||
\(93\) | −6.92820 | −0.718421 | ||||||||
\(94\) | 6.92820 | 0.714590 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −11.8564 | −1.20384 | −0.601918 | − | 0.798558i | \(-0.705597\pi\) | ||||
−0.601918 | + | 0.798558i | \(0.705597\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.8564 | 1.17976 | 0.589878 | − | 0.807492i | \(-0.299176\pi\) | ||||
0.589878 | + | 0.807492i | \(0.299176\pi\) | |||||||
\(102\) | 3.46410 | 0.342997 | ||||||||
\(103\) | 16.0000 | 1.57653 | 0.788263 | − | 0.615338i | \(-0.210980\pi\) | ||||
0.788263 | + | 0.615338i | \(0.210980\pi\) | |||||||
\(104\) | 3.46410 | 0.339683 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 12.9282 | 1.25570 | ||||||||
\(107\) | −6.92820 | −0.669775 | −0.334887 | − | 0.942258i | \(-0.608698\pi\) | ||||
−0.334887 | + | 0.942258i | \(0.608698\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 14.3923 | 1.37853 | 0.689266 | − | 0.724508i | \(-0.257933\pi\) | ||||
0.689266 | + | 0.724508i | \(0.257933\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −7.46410 | −0.708461 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 11.4641 | 1.07845 | 0.539226 | − | 0.842161i | \(-0.318717\pi\) | ||||
0.539226 | + | 0.842161i | \(0.318717\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.46410 | 0.136528 | ||||||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | 3.46410 | 0.320256 | ||||||||
\(118\) | −2.92820 | −0.269563 | ||||||||
\(119\) | −3.46410 | −0.317554 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −4.92820 | −0.446179 | ||||||||
\(123\) | 8.92820 | 0.805029 | ||||||||
\(124\) | 6.92820 | 0.622171 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 10.9282 | 0.969721 | 0.484861 | − | 0.874591i | \(-0.338870\pi\) | ||||
0.484861 | + | 0.874591i | \(0.338870\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.92820 | 0.257814 | ||||||||
\(130\) | −3.46410 | −0.303822 | ||||||||
\(131\) | −1.07180 | −0.0936433 | −0.0468217 | − | 0.998903i | \(-0.514909\pi\) | ||||
−0.0468217 | + | 0.998903i | \(0.514909\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.46410 | 0.817574 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −3.46410 | −0.297044 | ||||||||
\(137\) | −4.53590 | −0.387528 | −0.193764 | − | 0.981048i | \(-0.562070\pi\) | ||||
−0.193764 | + | 0.981048i | \(0.562070\pi\) | |||||||
\(138\) | 1.46410 | 0.124633 | ||||||||
\(139\) | −2.92820 | −0.248367 | −0.124183 | − | 0.992259i | \(-0.539631\pi\) | ||||
−0.124183 | + | 0.992259i | \(0.539631\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −6.92820 | −0.583460 | ||||||||
\(142\) | −4.00000 | −0.335673 | ||||||||
\(143\) | 3.46410 | 0.289683 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | −0.928203 | −0.0768186 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 7.46410 | 0.613545 | ||||||||
\(149\) | 12.9282 | 1.05912 | 0.529560 | − | 0.848273i | \(-0.322357\pi\) | ||||
0.529560 | + | 0.848273i | \(0.322357\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.46410 | −0.280056 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | −6.92820 | −0.556487 | ||||||||
\(156\) | −3.46410 | −0.277350 | ||||||||
\(157\) | −18.7846 | −1.49918 | −0.749588 | − | 0.661905i | \(-0.769748\pi\) | ||||
−0.749588 | + | 0.661905i | \(0.769748\pi\) | |||||||
\(158\) | 8.00000 | 0.636446 | ||||||||
\(159\) | −12.9282 | −1.02527 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −1.46410 | −0.115387 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 9.46410 | 0.741286 | 0.370643 | − | 0.928775i | \(-0.379137\pi\) | ||||
0.370643 | + | 0.928775i | \(0.379137\pi\) | |||||||
\(164\) | −8.92820 | −0.697176 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | 6.92820 | 0.537733 | ||||||||
\(167\) | −9.46410 | −0.732354 | −0.366177 | − | 0.930545i | \(-0.619334\pi\) | ||||
−0.366177 | + | 0.930545i | \(0.619334\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 3.46410 | 0.265684 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.92820 | −0.223273 | ||||||||
\(173\) | −8.92820 | −0.678799 | −0.339399 | − | 0.940642i | \(-0.610224\pi\) | ||||
−0.339399 | + | 0.940642i | \(0.610224\pi\) | |||||||
\(174\) | −2.00000 | −0.151620 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 2.92820 | 0.220097 | ||||||||
\(178\) | 3.46410 | 0.259645 | ||||||||
\(179\) | −20.7846 | −1.55351 | −0.776757 | − | 0.629800i | \(-0.783137\pi\) | ||||
−0.776757 | + | 0.629800i | \(0.783137\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | −16.5359 | −1.22910 | −0.614552 | − | 0.788876i | \(-0.710663\pi\) | ||||
−0.614552 | + | 0.788876i | \(0.710663\pi\) | |||||||
\(182\) | 3.46410 | 0.256776 | ||||||||
\(183\) | 4.92820 | 0.364303 | ||||||||
\(184\) | −1.46410 | −0.107935 | ||||||||
\(185\) | −7.46410 | −0.548772 | ||||||||
\(186\) | −6.92820 | −0.508001 | ||||||||
\(187\) | −3.46410 | −0.253320 | ||||||||
\(188\) | 6.92820 | 0.505291 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.9282 | 1.08017 | 0.540083 | − | 0.841611i | \(-0.318393\pi\) | ||||
0.540083 | + | 0.841611i | \(0.318393\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 11.0718 | 0.796965 | 0.398483 | − | 0.917176i | \(-0.369537\pi\) | ||||
0.398483 | + | 0.917176i | \(0.369537\pi\) | |||||||
\(194\) | −11.8564 | −0.851240 | ||||||||
\(195\) | 3.46410 | 0.248069 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −6.92820 | −0.491127 | −0.245564 | − | 0.969380i | \(-0.578973\pi\) | ||||
−0.245564 | + | 0.969380i | \(0.578973\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −9.46410 | −0.667546 | ||||||||
\(202\) | 11.8564 | 0.834214 | ||||||||
\(203\) | 2.00000 | 0.140372 | ||||||||
\(204\) | 3.46410 | 0.242536 | ||||||||
\(205\) | 8.92820 | 0.623573 | ||||||||
\(206\) | 16.0000 | 1.11477 | ||||||||
\(207\) | −1.46410 | −0.101762 | ||||||||
\(208\) | 3.46410 | 0.240192 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.00000 | 0.0690066 | ||||||||
\(211\) | −23.3205 | −1.60545 | −0.802725 | − | 0.596349i | \(-0.796617\pi\) | ||||
−0.802725 | + | 0.596349i | \(0.796617\pi\) | |||||||
\(212\) | 12.9282 | 0.887913 | ||||||||
\(213\) | 4.00000 | 0.274075 | ||||||||
\(214\) | −6.92820 | −0.473602 | ||||||||
\(215\) | 2.92820 | 0.199702 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 6.92820 | 0.470317 | ||||||||
\(218\) | 14.3923 | 0.974770 | ||||||||
\(219\) | 0.928203 | 0.0627222 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | −7.46410 | −0.500958 | ||||||||
\(223\) | 24.7846 | 1.65970 | 0.829850 | − | 0.557986i | \(-0.188426\pi\) | ||||
0.829850 | + | 0.557986i | \(0.188426\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 11.4641 | 0.762581 | ||||||||
\(227\) | 6.92820 | 0.459841 | 0.229920 | − | 0.973209i | \(-0.426153\pi\) | ||||
0.229920 | + | 0.973209i | \(0.426153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.39230 | 0.158088 | 0.0790440 | − | 0.996871i | \(-0.474813\pi\) | ||||
0.0790440 | + | 0.996871i | \(0.474813\pi\) | |||||||
\(230\) | 1.46410 | 0.0965400 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 2.00000 | 0.131306 | ||||||||
\(233\) | 2.00000 | 0.131024 | 0.0655122 | − | 0.997852i | \(-0.479132\pi\) | ||||
0.0655122 | + | 0.997852i | \(0.479132\pi\) | |||||||
\(234\) | 3.46410 | 0.226455 | ||||||||
\(235\) | −6.92820 | −0.451946 | ||||||||
\(236\) | −2.92820 | −0.190610 | ||||||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | −3.46410 | −0.224544 | ||||||||
\(239\) | 4.39230 | 0.284115 | 0.142057 | − | 0.989858i | \(-0.454628\pi\) | ||||
0.142057 | + | 0.989858i | \(0.454628\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −7.07180 | −0.455534 | −0.227767 | − | 0.973716i | \(-0.573143\pi\) | ||||
−0.227767 | + | 0.973716i | \(0.573143\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.92820 | −0.315496 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 8.92820 | 0.569241 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.92820 | 0.439941 | ||||||||
\(249\) | −6.92820 | −0.439057 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −5.07180 | −0.320129 | −0.160064 | − | 0.987107i | \(-0.551170\pi\) | ||||
−0.160064 | + | 0.987107i | \(0.551170\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −1.46410 | −0.0920473 | ||||||||
\(254\) | 10.9282 | 0.685696 | ||||||||
\(255\) | −3.46410 | −0.216930 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.9282 | −1.05595 | −0.527976 | − | 0.849259i | \(-0.677049\pi\) | ||||
−0.527976 | + | 0.849259i | \(0.677049\pi\) | |||||||
\(258\) | 2.92820 | 0.182302 | ||||||||
\(259\) | 7.46410 | 0.463797 | ||||||||
\(260\) | −3.46410 | −0.214834 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | −1.07180 | −0.0662158 | ||||||||
\(263\) | −16.7846 | −1.03498 | −0.517492 | − | 0.855688i | \(-0.673134\pi\) | ||||
−0.517492 | + | 0.855688i | \(0.673134\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −12.9282 | −0.794173 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.46410 | −0.212000 | ||||||||
\(268\) | 9.46410 | 0.578112 | ||||||||
\(269\) | −16.9282 | −1.03213 | −0.516065 | − | 0.856549i | \(-0.672604\pi\) | ||||
−0.516065 | + | 0.856549i | \(0.672604\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −5.85641 | −0.355751 | −0.177876 | − | 0.984053i | \(-0.556922\pi\) | ||||
−0.177876 | + | 0.984053i | \(0.556922\pi\) | |||||||
\(272\) | −3.46410 | −0.210042 | ||||||||
\(273\) | −3.46410 | −0.209657 | ||||||||
\(274\) | −4.53590 | −0.274024 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 1.46410 | 0.0881286 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | −2.92820 | −0.175622 | ||||||||
\(279\) | 6.92820 | 0.414781 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −14.3923 | −0.858573 | −0.429286 | − | 0.903168i | \(-0.641235\pi\) | ||||
−0.429286 | + | 0.903168i | \(0.641235\pi\) | |||||||
\(282\) | −6.92820 | −0.412568 | ||||||||
\(283\) | 1.46410 | 0.0870318 | 0.0435159 | − | 0.999053i | \(-0.486144\pi\) | ||||
0.0435159 | + | 0.999053i | \(0.486144\pi\) | |||||||
\(284\) | −4.00000 | −0.237356 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.46410 | 0.204837 | ||||||||
\(287\) | −8.92820 | −0.527015 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | −2.00000 | −0.117444 | ||||||||
\(291\) | 11.8564 | 0.695035 | ||||||||
\(292\) | −0.928203 | −0.0543190 | ||||||||
\(293\) | −14.0000 | −0.817889 | −0.408944 | − | 0.912559i | \(-0.634103\pi\) | ||||
−0.408944 | + | 0.912559i | \(0.634103\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 2.92820 | 0.170487 | ||||||||
\(296\) | 7.46410 | 0.433842 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 12.9282 | 0.748911 | ||||||||
\(299\) | −5.07180 | −0.293310 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −2.92820 | −0.168779 | ||||||||
\(302\) | 8.00000 | 0.460348 | ||||||||
\(303\) | −11.8564 | −0.681133 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.92820 | 0.282188 | ||||||||
\(306\) | −3.46410 | −0.198030 | ||||||||
\(307\) | 7.32051 | 0.417803 | 0.208902 | − | 0.977937i | \(-0.433011\pi\) | ||||
0.208902 | + | 0.977937i | \(0.433011\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | −16.0000 | −0.910208 | ||||||||
\(310\) | −6.92820 | −0.393496 | ||||||||
\(311\) | 6.53590 | 0.370617 | 0.185308 | − | 0.982680i | \(-0.440672\pi\) | ||||
0.185308 | + | 0.982680i | \(0.440672\pi\) | |||||||
\(312\) | −3.46410 | −0.196116 | ||||||||
\(313\) | 21.7128 | 1.22728 | 0.613640 | − | 0.789586i | \(-0.289704\pi\) | ||||
0.613640 | + | 0.789586i | \(0.289704\pi\) | |||||||
\(314\) | −18.7846 | −1.06008 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | −3.07180 | −0.172529 | −0.0862646 | − | 0.996272i | \(-0.527493\pi\) | ||||
−0.0862646 | + | 0.996272i | \(0.527493\pi\) | |||||||
\(318\) | −12.9282 | −0.724978 | ||||||||
\(319\) | 2.00000 | 0.111979 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 6.92820 | 0.386695 | ||||||||
\(322\) | −1.46410 | −0.0815912 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 3.46410 | 0.192154 | ||||||||
\(326\) | 9.46410 | 0.524168 | ||||||||
\(327\) | −14.3923 | −0.795896 | ||||||||
\(328\) | −8.92820 | −0.492978 | ||||||||
\(329\) | 6.92820 | 0.381964 | ||||||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 6.92820 | 0.380235 | ||||||||
\(333\) | 7.46410 | 0.409030 | ||||||||
\(334\) | −9.46410 | −0.517853 | ||||||||
\(335\) | −9.46410 | −0.517079 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 22.7846 | 1.24116 | 0.620578 | − | 0.784144i | \(-0.286898\pi\) | ||||
0.620578 | + | 0.784144i | \(0.286898\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −11.4641 | −0.622645 | ||||||||
\(340\) | 3.46410 | 0.187867 | ||||||||
\(341\) | 6.92820 | 0.375183 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.92820 | −0.157878 | ||||||||
\(345\) | −1.46410 | −0.0788246 | ||||||||
\(346\) | −8.92820 | −0.479983 | ||||||||
\(347\) | −1.07180 | −0.0575371 | −0.0287685 | − | 0.999586i | \(-0.509159\pi\) | ||||
−0.0287685 | + | 0.999586i | \(0.509159\pi\) | |||||||
\(348\) | −2.00000 | −0.107211 | ||||||||
\(349\) | −28.9282 | −1.54849 | −0.774246 | − | 0.632885i | \(-0.781870\pi\) | ||||
−0.774246 | + | 0.632885i | \(0.781870\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −3.46410 | −0.184900 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 20.9282 | 1.11390 | 0.556948 | − | 0.830547i | \(-0.311972\pi\) | ||||
0.556948 | + | 0.830547i | \(0.311972\pi\) | |||||||
\(354\) | 2.92820 | 0.155632 | ||||||||
\(355\) | 4.00000 | 0.212298 | ||||||||
\(356\) | 3.46410 | 0.183597 | ||||||||
\(357\) | 3.46410 | 0.183340 | ||||||||
\(358\) | −20.7846 | −1.09850 | ||||||||
\(359\) | 9.46410 | 0.499496 | 0.249748 | − | 0.968311i | \(-0.419652\pi\) | ||||
0.249748 | + | 0.968311i | \(0.419652\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | −16.5359 | −0.869108 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 3.46410 | 0.181568 | ||||||||
\(365\) | 0.928203 | 0.0485844 | ||||||||
\(366\) | 4.92820 | 0.257601 | ||||||||
\(367\) | 16.0000 | 0.835193 | 0.417597 | − | 0.908633i | \(-0.362873\pi\) | ||||
0.417597 | + | 0.908633i | \(0.362873\pi\) | |||||||
\(368\) | −1.46410 | −0.0763216 | ||||||||
\(369\) | −8.92820 | −0.464784 | ||||||||
\(370\) | −7.46410 | −0.388040 | ||||||||
\(371\) | 12.9282 | 0.671199 | ||||||||
\(372\) | −6.92820 | −0.359211 | ||||||||
\(373\) | −4.92820 | −0.255173 | −0.127586 | − | 0.991827i | \(-0.540723\pi\) | ||||
−0.127586 | + | 0.991827i | \(0.540723\pi\) | |||||||
\(374\) | −3.46410 | −0.179124 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 6.92820 | 0.357295 | ||||||||
\(377\) | 6.92820 | 0.356821 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9282 | −0.559869 | ||||||||
\(382\) | 14.9282 | 0.763793 | ||||||||
\(383\) | −12.7846 | −0.653263 | −0.326632 | − | 0.945152i | \(-0.605914\pi\) | ||||
−0.326632 | + | 0.945152i | \(0.605914\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | 11.0718 | 0.563540 | ||||||||
\(387\) | −2.92820 | −0.148849 | ||||||||
\(388\) | −11.8564 | −0.601918 | ||||||||
\(389\) | 21.7128 | 1.10088 | 0.550442 | − | 0.834874i | \(-0.314459\pi\) | ||||
0.550442 | + | 0.834874i | \(0.314459\pi\) | |||||||
\(390\) | 3.46410 | 0.175412 | ||||||||
\(391\) | 5.07180 | 0.256492 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 1.07180 | 0.0540650 | ||||||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −10.0000 | −0.501886 | −0.250943 | − | 0.968002i | \(-0.580741\pi\) | ||||
−0.250943 | + | 0.968002i | \(0.580741\pi\) | |||||||
\(398\) | −6.92820 | −0.347279 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −25.7128 | −1.28404 | −0.642018 | − | 0.766689i | \(-0.721903\pi\) | ||||
−0.642018 | + | 0.766689i | \(0.721903\pi\) | |||||||
\(402\) | −9.46410 | −0.472026 | ||||||||
\(403\) | 24.0000 | 1.19553 | ||||||||
\(404\) | 11.8564 | 0.589878 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 2.00000 | 0.0992583 | ||||||||
\(407\) | 7.46410 | 0.369982 | ||||||||
\(408\) | 3.46410 | 0.171499 | ||||||||
\(409\) | −12.9282 | −0.639259 | −0.319629 | − | 0.947543i | \(-0.603558\pi\) | ||||
−0.319629 | + | 0.947543i | \(0.603558\pi\) | |||||||
\(410\) | 8.92820 | 0.440933 | ||||||||
\(411\) | 4.53590 | 0.223739 | ||||||||
\(412\) | 16.0000 | 0.788263 | ||||||||
\(413\) | −2.92820 | −0.144087 | ||||||||
\(414\) | −1.46410 | −0.0719567 | ||||||||
\(415\) | −6.92820 | −0.340092 | ||||||||
\(416\) | 3.46410 | 0.169842 | ||||||||
\(417\) | 2.92820 | 0.143395 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.8564 | 0.676930 | 0.338465 | − | 0.940979i | \(-0.390092\pi\) | ||||
0.338465 | + | 0.940979i | \(0.390092\pi\) | |||||||
\(420\) | 1.00000 | 0.0487950 | ||||||||
\(421\) | −26.0000 | −1.26716 | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | −23.3205 | −1.13522 | ||||||||
\(423\) | 6.92820 | 0.336861 | ||||||||
\(424\) | 12.9282 | 0.627849 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 4.00000 | 0.193801 | ||||||||
\(427\) | −4.92820 | −0.238492 | ||||||||
\(428\) | −6.92820 | −0.334887 | ||||||||
\(429\) | −3.46410 | −0.167248 | ||||||||
\(430\) | 2.92820 | 0.141210 | ||||||||
\(431\) | −23.3205 | −1.12331 | −0.561655 | − | 0.827372i | \(-0.689835\pi\) | ||||
−0.561655 | + | 0.827372i | \(0.689835\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −17.7128 | −0.851223 | −0.425612 | − | 0.904906i | \(-0.639941\pi\) | ||||
−0.425612 | + | 0.904906i | \(0.639941\pi\) | |||||||
\(434\) | 6.92820 | 0.332564 | ||||||||
\(435\) | 2.00000 | 0.0958927 | ||||||||
\(436\) | 14.3923 | 0.689266 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.928203 | 0.0443513 | ||||||||
\(439\) | −16.7846 | −0.801086 | −0.400543 | − | 0.916278i | \(-0.631178\pi\) | ||||
−0.400543 | + | 0.916278i | \(0.631178\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | 26.9282 | 1.27940 | 0.639699 | − | 0.768626i | \(-0.279059\pi\) | ||||
0.639699 | + | 0.768626i | \(0.279059\pi\) | |||||||
\(444\) | −7.46410 | −0.354231 | ||||||||
\(445\) | −3.46410 | −0.164214 | ||||||||
\(446\) | 24.7846 | 1.17359 | ||||||||
\(447\) | −12.9282 | −0.611483 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −22.0000 | −1.03824 | −0.519122 | − | 0.854700i | \(-0.673741\pi\) | ||||
−0.519122 | + | 0.854700i | \(0.673741\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −8.92820 | −0.420413 | ||||||||
\(452\) | 11.4641 | 0.539226 | ||||||||
\(453\) | −8.00000 | −0.375873 | ||||||||
\(454\) | 6.92820 | 0.325157 | ||||||||
\(455\) | −3.46410 | −0.162400 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.0718 | 0.892141 | 0.446071 | − | 0.894998i | \(-0.352823\pi\) | ||||
0.446071 | + | 0.894998i | \(0.352823\pi\) | |||||||
\(458\) | 2.39230 | 0.111785 | ||||||||
\(459\) | 3.46410 | 0.161690 | ||||||||
\(460\) | 1.46410 | 0.0682641 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | −1.00000 | −0.0465242 | ||||||||
\(463\) | 20.7846 | 0.965943 | 0.482971 | − | 0.875636i | \(-0.339558\pi\) | ||||
0.482971 | + | 0.875636i | \(0.339558\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 6.92820 | 0.321288 | ||||||||
\(466\) | 2.00000 | 0.0926482 | ||||||||
\(467\) | −30.9282 | −1.43119 | −0.715593 | − | 0.698517i | \(-0.753844\pi\) | ||||
−0.715593 | + | 0.698517i | \(0.753844\pi\) | |||||||
\(468\) | 3.46410 | 0.160128 | ||||||||
\(469\) | 9.46410 | 0.437012 | ||||||||
\(470\) | −6.92820 | −0.319574 | ||||||||
\(471\) | 18.7846 | 0.865549 | ||||||||
\(472\) | −2.92820 | −0.134781 | ||||||||
\(473\) | −2.92820 | −0.134639 | ||||||||
\(474\) | −8.00000 | −0.367452 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.46410 | −0.158777 | ||||||||
\(477\) | 12.9282 | 0.591942 | ||||||||
\(478\) | 4.39230 | 0.200899 | ||||||||
\(479\) | 13.8564 | 0.633115 | 0.316558 | − | 0.948573i | \(-0.397473\pi\) | ||||
0.316558 | + | 0.948573i | \(0.397473\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 25.8564 | 1.17895 | ||||||||
\(482\) | −7.07180 | −0.322112 | ||||||||
\(483\) | 1.46410 | 0.0666189 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 11.8564 | 0.538372 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 1.07180 | 0.0485677 | 0.0242839 | − | 0.999705i | \(-0.492269\pi\) | ||||
0.0242839 | + | 0.999705i | \(0.492269\pi\) | |||||||
\(488\) | −4.92820 | −0.223089 | ||||||||
\(489\) | −9.46410 | −0.427981 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 1.85641 | 0.0837785 | 0.0418892 | − | 0.999122i | \(-0.486662\pi\) | ||||
0.0418892 | + | 0.999122i | \(0.486662\pi\) | |||||||
\(492\) | 8.92820 | 0.402514 | ||||||||
\(493\) | −6.92820 | −0.312031 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 6.92820 | 0.311086 | ||||||||
\(497\) | −4.00000 | −0.179425 | ||||||||
\(498\) | −6.92820 | −0.310460 | ||||||||
\(499\) | 17.0718 | 0.764239 | 0.382119 | − | 0.924113i | \(-0.375194\pi\) | ||||
0.382119 | + | 0.924113i | \(0.375194\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 9.46410 | 0.422825 | ||||||||
\(502\) | −5.07180 | −0.226365 | ||||||||
\(503\) | 12.3923 | 0.552546 | 0.276273 | − | 0.961079i | \(-0.410901\pi\) | ||||
0.276273 | + | 0.961079i | \(0.410901\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −11.8564 | −0.527603 | ||||||||
\(506\) | −1.46410 | −0.0650873 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 10.9282 | 0.484861 | ||||||||
\(509\) | −32.9282 | −1.45952 | −0.729758 | − | 0.683705i | \(-0.760367\pi\) | ||||
−0.729758 | + | 0.683705i | \(0.760367\pi\) | |||||||
\(510\) | −3.46410 | −0.153393 | ||||||||
\(511\) | −0.928203 | −0.0410613 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16.9282 | −0.746671 | ||||||||
\(515\) | −16.0000 | −0.705044 | ||||||||
\(516\) | 2.92820 | 0.128907 | ||||||||
\(517\) | 6.92820 | 0.304702 | ||||||||
\(518\) | 7.46410 | 0.327954 | ||||||||
\(519\) | 8.92820 | 0.391905 | ||||||||
\(520\) | −3.46410 | −0.151911 | ||||||||
\(521\) | 27.4641 | 1.20322 | 0.601612 | − | 0.798788i | \(-0.294525\pi\) | ||||
0.601612 | + | 0.798788i | \(0.294525\pi\) | |||||||
\(522\) | 2.00000 | 0.0875376 | ||||||||
\(523\) | 44.3923 | 1.94114 | 0.970570 | − | 0.240819i | \(-0.0774161\pi\) | ||||
0.970570 | + | 0.240819i | \(0.0774161\pi\) | |||||||
\(524\) | −1.07180 | −0.0468217 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | −16.7846 | −0.731844 | ||||||||
\(527\) | −24.0000 | −1.04546 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −20.8564 | −0.906800 | ||||||||
\(530\) | −12.9282 | −0.561565 | ||||||||
\(531\) | −2.92820 | −0.127073 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.9282 | −1.33965 | ||||||||
\(534\) | −3.46410 | −0.149906 | ||||||||
\(535\) | 6.92820 | 0.299532 | ||||||||
\(536\) | 9.46410 | 0.408787 | ||||||||
\(537\) | 20.7846 | 0.896922 | ||||||||
\(538\) | −16.9282 | −0.729827 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 9.32051 | 0.400720 | 0.200360 | − | 0.979722i | \(-0.435789\pi\) | ||||
0.200360 | + | 0.979722i | \(0.435789\pi\) | |||||||
\(542\) | −5.85641 | −0.251554 | ||||||||
\(543\) | 16.5359 | 0.709623 | ||||||||
\(544\) | −3.46410 | −0.148522 | ||||||||
\(545\) | −14.3923 | −0.616499 | ||||||||
\(546\) | −3.46410 | −0.148250 | ||||||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | −4.53590 | −0.193764 | ||||||||
\(549\) | −4.92820 | −0.210331 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.46410 | 0.0623163 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | −10.0000 | −0.424859 | ||||||||
\(555\) | 7.46410 | 0.316833 | ||||||||
\(556\) | −2.92820 | −0.124183 | ||||||||
\(557\) | −31.8564 | −1.34980 | −0.674900 | − | 0.737910i | \(-0.735813\pi\) | ||||
−0.674900 | + | 0.737910i | \(0.735813\pi\) | |||||||
\(558\) | 6.92820 | 0.293294 | ||||||||
\(559\) | −10.1436 | −0.429028 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 3.46410 | 0.146254 | ||||||||
\(562\) | −14.3923 | −0.607103 | ||||||||
\(563\) | −31.7128 | −1.33654 | −0.668268 | − | 0.743921i | \(-0.732964\pi\) | ||||
−0.668268 | + | 0.743921i | \(0.732964\pi\) | |||||||
\(564\) | −6.92820 | −0.291730 | ||||||||
\(565\) | −11.4641 | −0.482298 | ||||||||
\(566\) | 1.46410 | 0.0615408 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −39.1769 | −1.64238 | −0.821191 | − | 0.570654i | \(-0.806690\pi\) | ||||
−0.821191 | + | 0.570654i | \(0.806690\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.3205 | 0.975933 | 0.487966 | − | 0.872862i | \(-0.337739\pi\) | ||||
0.487966 | + | 0.872862i | \(0.337739\pi\) | |||||||
\(572\) | 3.46410 | 0.144841 | ||||||||
\(573\) | −14.9282 | −0.623635 | ||||||||
\(574\) | −8.92820 | −0.372656 | ||||||||
\(575\) | −1.46410 | −0.0610573 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 45.7128 | 1.90305 | 0.951525 | − | 0.307572i | \(-0.0995167\pi\) | ||||
0.951525 | + | 0.307572i | \(0.0995167\pi\) | |||||||
\(578\) | −5.00000 | −0.207973 | ||||||||
\(579\) | −11.0718 | −0.460128 | ||||||||
\(580\) | −2.00000 | −0.0830455 | ||||||||
\(581\) | 6.92820 | 0.287430 | ||||||||
\(582\) | 11.8564 | 0.491464 | ||||||||
\(583\) | 12.9282 | 0.535431 | ||||||||
\(584\) | −0.928203 | −0.0384093 | ||||||||
\(585\) | −3.46410 | −0.143223 | ||||||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | −20.7846 | −0.857873 | −0.428936 | − | 0.903335i | \(-0.641112\pi\) | ||||
−0.428936 | + | 0.903335i | \(0.641112\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 2.92820 | 0.120552 | ||||||||
\(591\) | 18.0000 | 0.740421 | ||||||||
\(592\) | 7.46410 | 0.306773 | ||||||||
\(593\) | 27.1769 | 1.11602 | 0.558011 | − | 0.829834i | \(-0.311565\pi\) | ||||
0.558011 | + | 0.829834i | \(0.311565\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 3.46410 | 0.142014 | ||||||||
\(596\) | 12.9282 | 0.529560 | ||||||||
\(597\) | 6.92820 | 0.283552 | ||||||||
\(598\) | −5.07180 | −0.207401 | ||||||||
\(599\) | −3.21539 | −0.131377 | −0.0656886 | − | 0.997840i | \(-0.520924\pi\) | ||||
−0.0656886 | + | 0.997840i | \(0.520924\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −23.0718 | −0.941118 | −0.470559 | − | 0.882368i | \(-0.655948\pi\) | ||||
−0.470559 | + | 0.882368i | \(0.655948\pi\) | |||||||
\(602\) | −2.92820 | −0.119345 | ||||||||
\(603\) | 9.46410 | 0.385408 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −11.8564 | −0.481634 | ||||||||
\(607\) | 16.0000 | 0.649420 | 0.324710 | − | 0.945814i | \(-0.394733\pi\) | ||||
0.324710 | + | 0.945814i | \(0.394733\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.00000 | −0.0810441 | ||||||||
\(610\) | 4.92820 | 0.199537 | ||||||||
\(611\) | 24.0000 | 0.970936 | ||||||||
\(612\) | −3.46410 | −0.140028 | ||||||||
\(613\) | −2.00000 | −0.0807792 | −0.0403896 | − | 0.999184i | \(-0.512860\pi\) | ||||
−0.0403896 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(614\) | 7.32051 | 0.295432 | ||||||||
\(615\) | −8.92820 | −0.360020 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −2.39230 | −0.0963106 | −0.0481553 | − | 0.998840i | \(-0.515334\pi\) | ||||
−0.0481553 | + | 0.998840i | \(0.515334\pi\) | |||||||
\(618\) | −16.0000 | −0.643614 | ||||||||
\(619\) | 15.3205 | 0.615783 | 0.307892 | − | 0.951421i | \(-0.400377\pi\) | ||||
0.307892 | + | 0.951421i | \(0.400377\pi\) | |||||||
\(620\) | −6.92820 | −0.278243 | ||||||||
\(621\) | 1.46410 | 0.0587524 | ||||||||
\(622\) | 6.53590 | 0.262066 | ||||||||
\(623\) | 3.46410 | 0.138786 | ||||||||
\(624\) | −3.46410 | −0.138675 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 21.7128 | 0.867819 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18.7846 | −0.749588 | ||||||||
\(629\) | −25.8564 | −1.03096 | ||||||||
\(630\) | −1.00000 | −0.0398410 | ||||||||
\(631\) | 16.7846 | 0.668185 | 0.334092 | − | 0.942540i | \(-0.391570\pi\) | ||||
0.334092 | + | 0.942540i | \(0.391570\pi\) | |||||||
\(632\) | 8.00000 | 0.318223 | ||||||||
\(633\) | 23.3205 | 0.926907 | ||||||||
\(634\) | −3.07180 | −0.121997 | ||||||||
\(635\) | −10.9282 | −0.433673 | ||||||||
\(636\) | −12.9282 | −0.512637 | ||||||||
\(637\) | 3.46410 | 0.137253 | ||||||||
\(638\) | 2.00000 | 0.0791808 | ||||||||
\(639\) | −4.00000 | −0.158238 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −6.00000 | −0.236986 | −0.118493 | − | 0.992955i | \(-0.537806\pi\) | ||||
−0.118493 | + | 0.992955i | \(0.537806\pi\) | |||||||
\(642\) | 6.92820 | 0.273434 | ||||||||
\(643\) | −23.7128 | −0.935142 | −0.467571 | − | 0.883956i | \(-0.654871\pi\) | ||||
−0.467571 | + | 0.883956i | \(0.654871\pi\) | |||||||
\(644\) | −1.46410 | −0.0576937 | ||||||||
\(645\) | −2.92820 | −0.115298 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.9282 | −0.901401 | −0.450700 | − | 0.892675i | \(-0.648826\pi\) | ||||
−0.450700 | + | 0.892675i | \(0.648826\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −2.92820 | −0.114942 | ||||||||
\(650\) | 3.46410 | 0.135873 | ||||||||
\(651\) | −6.92820 | −0.271538 | ||||||||
\(652\) | 9.46410 | 0.370643 | ||||||||
\(653\) | 31.8564 | 1.24664 | 0.623319 | − | 0.781968i | \(-0.285784\pi\) | ||||
0.623319 | + | 0.781968i | \(0.285784\pi\) | |||||||
\(654\) | −14.3923 | −0.562784 | ||||||||
\(655\) | 1.07180 | 0.0418786 | ||||||||
\(656\) | −8.92820 | −0.348588 | ||||||||
\(657\) | −0.928203 | −0.0362127 | ||||||||
\(658\) | 6.92820 | 0.270089 | ||||||||
\(659\) | −39.7128 | −1.54699 | −0.773496 | − | 0.633801i | \(-0.781494\pi\) | ||||
−0.773496 | + | 0.633801i | \(0.781494\pi\) | |||||||
\(660\) | 1.00000 | 0.0389249 | ||||||||
\(661\) | 1.60770 | 0.0625321 | 0.0312660 | − | 0.999511i | \(-0.490046\pi\) | ||||
0.0312660 | + | 0.999511i | \(0.490046\pi\) | |||||||
\(662\) | −4.00000 | −0.155464 | ||||||||
\(663\) | 12.0000 | 0.466041 | ||||||||
\(664\) | 6.92820 | 0.268866 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.46410 | 0.289228 | ||||||||
\(667\) | −2.92820 | −0.113380 | ||||||||
\(668\) | −9.46410 | −0.366177 | ||||||||
\(669\) | −24.7846 | −0.958228 | ||||||||
\(670\) | −9.46410 | −0.365630 | ||||||||
\(671\) | −4.92820 | −0.190251 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −15.0718 | −0.580975 | −0.290488 | − | 0.956879i | \(-0.593817\pi\) | ||||
−0.290488 | + | 0.956879i | \(0.593817\pi\) | |||||||
\(674\) | 22.7846 | 0.877630 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −1.00000 | −0.0384615 | ||||||||
\(677\) | −40.9282 | −1.57300 | −0.786499 | − | 0.617591i | \(-0.788109\pi\) | ||||
−0.786499 | + | 0.617591i | \(0.788109\pi\) | |||||||
\(678\) | −11.4641 | −0.440276 | ||||||||
\(679\) | −11.8564 | −0.455007 | ||||||||
\(680\) | 3.46410 | 0.132842 | ||||||||
\(681\) | −6.92820 | −0.265489 | ||||||||
\(682\) | 6.92820 | 0.265295 | ||||||||
\(683\) | 26.9282 | 1.03038 | 0.515190 | − | 0.857076i | \(-0.327722\pi\) | ||||
0.515190 | + | 0.857076i | \(0.327722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.53590 | 0.173308 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −2.39230 | −0.0912721 | ||||||||
\(688\) | −2.92820 | −0.111637 | ||||||||
\(689\) | 44.7846 | 1.70616 | ||||||||
\(690\) | −1.46410 | −0.0557374 | ||||||||
\(691\) | 3.60770 | 0.137243 | 0.0686216 | − | 0.997643i | \(-0.478140\pi\) | ||||
0.0686216 | + | 0.997643i | \(0.478140\pi\) | |||||||
\(692\) | −8.92820 | −0.339399 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | −1.07180 | −0.0406848 | ||||||||
\(695\) | 2.92820 | 0.111073 | ||||||||
\(696\) | −2.00000 | −0.0758098 | ||||||||
\(697\) | 30.9282 | 1.17149 | ||||||||
\(698\) | −28.9282 | −1.09495 | ||||||||
\(699\) | −2.00000 | −0.0756469 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | −3.46410 | −0.130744 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 6.92820 | 0.260931 | ||||||||
\(706\) | 20.9282 | 0.787643 | ||||||||
\(707\) | 11.8564 | 0.445906 | ||||||||
\(708\) | 2.92820 | 0.110049 | ||||||||
\(709\) | −7.85641 | −0.295054 | −0.147527 | − | 0.989058i | \(-0.547131\pi\) | ||||
−0.147527 | + | 0.989058i | \(0.547131\pi\) | |||||||
\(710\) | 4.00000 | 0.150117 | ||||||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | 3.46410 | 0.129823 | ||||||||
\(713\) | −10.1436 | −0.379881 | ||||||||
\(714\) | 3.46410 | 0.129641 | ||||||||
\(715\) | −3.46410 | −0.129550 | ||||||||
\(716\) | −20.7846 | −0.776757 | ||||||||
\(717\) | −4.39230 | −0.164034 | ||||||||
\(718\) | 9.46410 | 0.353197 | ||||||||
\(719\) | −4.39230 | −0.163805 | −0.0819027 | − | 0.996640i | \(-0.526100\pi\) | ||||
−0.0819027 | + | 0.996640i | \(0.526100\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | −19.0000 | −0.707107 | ||||||||
\(723\) | 7.07180 | 0.263003 | ||||||||
\(724\) | −16.5359 | −0.614552 | ||||||||
\(725\) | 2.00000 | 0.0742781 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | 13.0718 | 0.484806 | 0.242403 | − | 0.970176i | \(-0.422064\pi\) | ||||
0.242403 | + | 0.970176i | \(0.422064\pi\) | |||||||
\(728\) | 3.46410 | 0.128388 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.928203 | 0.0343543 | ||||||||
\(731\) | 10.1436 | 0.375174 | ||||||||
\(732\) | 4.92820 | 0.182152 | ||||||||
\(733\) | −24.2487 | −0.895647 | −0.447823 | − | 0.894122i | \(-0.647801\pi\) | ||||
−0.447823 | + | 0.894122i | \(0.647801\pi\) | |||||||
\(734\) | 16.0000 | 0.590571 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | −1.46410 | −0.0539675 | ||||||||
\(737\) | 9.46410 | 0.348615 | ||||||||
\(738\) | −8.92820 | −0.328652 | ||||||||
\(739\) | 15.3205 | 0.563574 | 0.281787 | − | 0.959477i | \(-0.409073\pi\) | ||||
0.281787 | + | 0.959477i | \(0.409073\pi\) | |||||||
\(740\) | −7.46410 | −0.274386 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.9282 | 0.474609 | ||||||||
\(743\) | 13.8564 | 0.508342 | 0.254171 | − | 0.967159i | \(-0.418197\pi\) | ||||
0.254171 | + | 0.967159i | \(0.418197\pi\) | |||||||
\(744\) | −6.92820 | −0.254000 | ||||||||
\(745\) | −12.9282 | −0.473653 | ||||||||
\(746\) | −4.92820 | −0.180434 | ||||||||
\(747\) | 6.92820 | 0.253490 | ||||||||
\(748\) | −3.46410 | −0.126660 | ||||||||
\(749\) | −6.92820 | −0.253151 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −0.784610 | −0.0286308 | −0.0143154 | − | 0.999898i | \(-0.504557\pi\) | ||||
−0.0143154 | + | 0.999898i | \(0.504557\pi\) | |||||||
\(752\) | 6.92820 | 0.252646 | ||||||||
\(753\) | 5.07180 | 0.184827 | ||||||||
\(754\) | 6.92820 | 0.252310 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | −50.1051 | −1.82110 | −0.910551 | − | 0.413397i | \(-0.864342\pi\) | ||||
−0.910551 | + | 0.413397i | \(0.864342\pi\) | |||||||
\(758\) | −28.0000 | −1.01701 | ||||||||
\(759\) | 1.46410 | 0.0531435 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.7846 | −1.40594 | −0.702971 | − | 0.711219i | \(-0.748143\pi\) | ||||
−0.702971 | + | 0.711219i | \(0.748143\pi\) | |||||||
\(762\) | −10.9282 | −0.395887 | ||||||||
\(763\) | 14.3923 | 0.521036 | ||||||||
\(764\) | 14.9282 | 0.540083 | ||||||||
\(765\) | 3.46410 | 0.125245 | ||||||||
\(766\) | −12.7846 | −0.461927 | ||||||||
\(767\) | −10.1436 | −0.366264 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 38.7846 | 1.39861 | 0.699304 | − | 0.714824i | \(-0.253493\pi\) | ||||
0.699304 | + | 0.714824i | \(0.253493\pi\) | |||||||
\(770\) | −1.00000 | −0.0360375 | ||||||||
\(771\) | 16.9282 | 0.609654 | ||||||||
\(772\) | 11.0718 | 0.398483 | ||||||||
\(773\) | 26.0000 | 0.935155 | 0.467578 | − | 0.883952i | \(-0.345127\pi\) | ||||
0.467578 | + | 0.883952i | \(0.345127\pi\) | |||||||
\(774\) | −2.92820 | −0.105252 | ||||||||
\(775\) | 6.92820 | 0.248868 | ||||||||
\(776\) | −11.8564 | −0.425620 | ||||||||
\(777\) | −7.46410 | −0.267773 | ||||||||
\(778\) | 21.7128 | 0.778442 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 3.46410 | 0.124035 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 5.07180 | 0.181367 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 18.7846 | 0.670451 | ||||||||
\(786\) | 1.07180 | 0.0382297 | ||||||||
\(787\) | 41.4641 | 1.47804 | 0.739018 | − | 0.673686i | \(-0.235290\pi\) | ||||
0.739018 | + | 0.673686i | \(0.235290\pi\) | |||||||
\(788\) | −18.0000 | −0.641223 | ||||||||
\(789\) | 16.7846 | 0.597548 | ||||||||
\(790\) | −8.00000 | −0.284627 | ||||||||
\(791\) | 11.4641 | 0.407617 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −17.0718 | −0.606237 | ||||||||
\(794\) | −10.0000 | −0.354887 | ||||||||
\(795\) | 12.9282 | 0.458516 | ||||||||
\(796\) | −6.92820 | −0.245564 | ||||||||
\(797\) | 31.8564 | 1.12841 | 0.564206 | − | 0.825634i | \(-0.309182\pi\) | ||||
0.564206 | + | 0.825634i | \(0.309182\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 3.46410 | 0.122398 | ||||||||
\(802\) | −25.7128 | −0.907951 | ||||||||
\(803\) | −0.928203 | −0.0327556 | ||||||||
\(804\) | −9.46410 | −0.333773 | ||||||||
\(805\) | 1.46410 | 0.0516028 | ||||||||
\(806\) | 24.0000 | 0.845364 | ||||||||
\(807\) | 16.9282 | 0.595901 | ||||||||
\(808\) | 11.8564 | 0.417107 | ||||||||
\(809\) | −11.4641 | −0.403056 | −0.201528 | − | 0.979483i | \(-0.564591\pi\) | ||||
−0.201528 | + | 0.979483i | \(0.564591\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 13.8564 | 0.486564 | 0.243282 | − | 0.969956i | \(-0.421776\pi\) | ||||
0.243282 | + | 0.969956i | \(0.421776\pi\) | |||||||
\(812\) | 2.00000 | 0.0701862 | ||||||||
\(813\) | 5.85641 | 0.205393 | ||||||||
\(814\) | 7.46410 | 0.261617 | ||||||||
\(815\) | −9.46410 | −0.331513 | ||||||||
\(816\) | 3.46410 | 0.121268 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −12.9282 | −0.452024 | ||||||||
\(819\) | 3.46410 | 0.121046 | ||||||||
\(820\) | 8.92820 | 0.311786 | ||||||||
\(821\) | 12.1436 | 0.423814 | 0.211907 | − | 0.977290i | \(-0.432033\pi\) | ||||
0.211907 | + | 0.977290i | \(0.432033\pi\) | |||||||
\(822\) | 4.53590 | 0.158208 | ||||||||
\(823\) | 49.8564 | 1.73789 | 0.868943 | − | 0.494913i | \(-0.164800\pi\) | ||||
0.868943 | + | 0.494913i | \(0.164800\pi\) | |||||||
\(824\) | 16.0000 | 0.557386 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | −2.92820 | −0.101885 | ||||||||
\(827\) | 20.7846 | 0.722752 | 0.361376 | − | 0.932420i | \(-0.382307\pi\) | ||||
0.361376 | + | 0.932420i | \(0.382307\pi\) | |||||||
\(828\) | −1.46410 | −0.0508810 | ||||||||
\(829\) | 51.1769 | 1.77745 | 0.888724 | − | 0.458443i | \(-0.151593\pi\) | ||||
0.888724 | + | 0.458443i | \(0.151593\pi\) | |||||||
\(830\) | −6.92820 | −0.240481 | ||||||||
\(831\) | 10.0000 | 0.346896 | ||||||||
\(832\) | 3.46410 | 0.120096 | ||||||||
\(833\) | −3.46410 | −0.120024 | ||||||||
\(834\) | 2.92820 | 0.101395 | ||||||||
\(835\) | 9.46410 | 0.327519 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.92820 | −0.239474 | ||||||||
\(838\) | 13.8564 | 0.478662 | ||||||||
\(839\) | 30.5359 | 1.05422 | 0.527108 | − | 0.849798i | \(-0.323276\pi\) | ||||
0.527108 | + | 0.849798i | \(0.323276\pi\) | |||||||
\(840\) | 1.00000 | 0.0345033 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −26.0000 | −0.896019 | ||||||||
\(843\) | 14.3923 | 0.495697 | ||||||||
\(844\) | −23.3205 | −0.802725 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 6.92820 | 0.238197 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 12.9282 | 0.443956 | ||||||||
\(849\) | −1.46410 | −0.0502478 | ||||||||
\(850\) | −3.46410 | −0.118818 | ||||||||
\(851\) | −10.9282 | −0.374614 | ||||||||
\(852\) | 4.00000 | 0.137038 | ||||||||
\(853\) | 15.1769 | 0.519648 | 0.259824 | − | 0.965656i | \(-0.416336\pi\) | ||||
0.259824 | + | 0.965656i | \(0.416336\pi\) | |||||||
\(854\) | −4.92820 | −0.168640 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.92820 | −0.236801 | ||||||||
\(857\) | −0.535898 | −0.0183059 | −0.00915297 | − | 0.999958i | \(-0.502914\pi\) | ||||
−0.00915297 | + | 0.999958i | \(0.502914\pi\) | |||||||
\(858\) | −3.46410 | −0.118262 | ||||||||
\(859\) | 20.3923 | 0.695776 | 0.347888 | − | 0.937536i | \(-0.386899\pi\) | ||||
0.347888 | + | 0.937536i | \(0.386899\pi\) | |||||||
\(860\) | 2.92820 | 0.0998509 | ||||||||
\(861\) | 8.92820 | 0.304272 | ||||||||
\(862\) | −23.3205 | −0.794300 | ||||||||
\(863\) | 42.2487 | 1.43816 | 0.719081 | − | 0.694926i | \(-0.244563\pi\) | ||||
0.719081 | + | 0.694926i | \(0.244563\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 8.92820 | 0.303568 | ||||||||
\(866\) | −17.7128 | −0.601906 | ||||||||
\(867\) | 5.00000 | 0.169809 | ||||||||
\(868\) | 6.92820 | 0.235159 | ||||||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 2.00000 | 0.0678064 | ||||||||
\(871\) | 32.7846 | 1.11086 | ||||||||
\(872\) | 14.3923 | 0.487385 | ||||||||
\(873\) | −11.8564 | −0.401279 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0.928203 | 0.0313611 | ||||||||
\(877\) | −7.85641 | −0.265292 | −0.132646 | − | 0.991163i | \(-0.542347\pi\) | ||||
−0.132646 | + | 0.991163i | \(0.542347\pi\) | |||||||
\(878\) | −16.7846 | −0.566453 | ||||||||
\(879\) | 14.0000 | 0.472208 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | 17.3205 | 0.583543 | 0.291771 | − | 0.956488i | \(-0.405755\pi\) | ||||
0.291771 | + | 0.956488i | \(0.405755\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −48.1051 | −1.61887 | −0.809433 | − | 0.587212i | \(-0.800225\pi\) | ||||
−0.809433 | + | 0.587212i | \(0.800225\pi\) | |||||||
\(884\) | −12.0000 | −0.403604 | ||||||||
\(885\) | −2.92820 | −0.0984305 | ||||||||
\(886\) | 26.9282 | 0.904671 | ||||||||
\(887\) | −16.6795 | −0.560043 | −0.280021 | − | 0.959994i | \(-0.590342\pi\) | ||||
−0.280021 | + | 0.959994i | \(0.590342\pi\) | |||||||
\(888\) | −7.46410 | −0.250479 | ||||||||
\(889\) | 10.9282 | 0.366520 | ||||||||
\(890\) | −3.46410 | −0.116117 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 24.7846 | 0.829850 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −12.9282 | −0.432384 | ||||||||
\(895\) | 20.7846 | 0.694753 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 5.07180 | 0.169342 | ||||||||
\(898\) | −22.0000 | −0.734150 | ||||||||
\(899\) | 13.8564 | 0.462137 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −44.7846 | −1.49199 | ||||||||
\(902\) | −8.92820 | −0.297277 | ||||||||
\(903\) | 2.92820 | 0.0974445 | ||||||||
\(904\) | 11.4641 | 0.381290 | ||||||||
\(905\) | 16.5359 | 0.549672 | ||||||||
\(906\) | −8.00000 | −0.265782 | ||||||||
\(907\) | −21.1769 | −0.703168 | −0.351584 | − | 0.936156i | \(-0.614357\pi\) | ||||
−0.351584 | + | 0.936156i | \(0.614357\pi\) | |||||||
\(908\) | 6.92820 | 0.229920 | ||||||||
\(909\) | 11.8564 | 0.393252 | ||||||||
\(910\) | −3.46410 | −0.114834 | ||||||||
\(911\) | −4.00000 | −0.132526 | −0.0662630 | − | 0.997802i | \(-0.521108\pi\) | ||||
−0.0662630 | + | 0.997802i | \(0.521108\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.92820 | 0.229290 | ||||||||
\(914\) | 19.0718 | 0.630839 | ||||||||
\(915\) | −4.92820 | −0.162921 | ||||||||
\(916\) | 2.39230 | 0.0790440 | ||||||||
\(917\) | −1.07180 | −0.0353938 | ||||||||
\(918\) | 3.46410 | 0.114332 | ||||||||
\(919\) | 45.0718 | 1.48678 | 0.743391 | − | 0.668857i | \(-0.233216\pi\) | ||||
0.743391 | + | 0.668857i | \(0.233216\pi\) | |||||||
\(920\) | 1.46410 | 0.0482700 | ||||||||
\(921\) | −7.32051 | −0.241219 | ||||||||
\(922\) | −18.0000 | −0.592798 | ||||||||
\(923\) | −13.8564 | −0.456089 | ||||||||
\(924\) | −1.00000 | −0.0328976 | ||||||||
\(925\) | 7.46410 | 0.245418 | ||||||||
\(926\) | 20.7846 | 0.683025 | ||||||||
\(927\) | 16.0000 | 0.525509 | ||||||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | −25.6077 | −0.840161 | −0.420081 | − | 0.907487i | \(-0.637998\pi\) | ||||
−0.420081 | + | 0.907487i | \(0.637998\pi\) | |||||||
\(930\) | 6.92820 | 0.227185 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.00000 | 0.0655122 | ||||||||
\(933\) | −6.53590 | −0.213976 | ||||||||
\(934\) | −30.9282 | −1.01200 | ||||||||
\(935\) | 3.46410 | 0.113288 | ||||||||
\(936\) | 3.46410 | 0.113228 | ||||||||
\(937\) | −3.85641 | −0.125983 | −0.0629917 | − | 0.998014i | \(-0.520064\pi\) | ||||
−0.0629917 | + | 0.998014i | \(0.520064\pi\) | |||||||
\(938\) | 9.46410 | 0.309014 | ||||||||
\(939\) | −21.7128 | −0.708571 | ||||||||
\(940\) | −6.92820 | −0.225973 | ||||||||
\(941\) | 22.0000 | 0.717180 | 0.358590 | − | 0.933495i | \(-0.383258\pi\) | ||||
0.358590 | + | 0.933495i | \(0.383258\pi\) | |||||||
\(942\) | 18.7846 | 0.612036 | ||||||||
\(943\) | 13.0718 | 0.425676 | ||||||||
\(944\) | −2.92820 | −0.0953049 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | −2.92820 | −0.0952041 | ||||||||
\(947\) | −10.1436 | −0.329622 | −0.164811 | − | 0.986325i | \(-0.552701\pi\) | ||||
−0.164811 | + | 0.986325i | \(0.552701\pi\) | |||||||
\(948\) | −8.00000 | −0.259828 | ||||||||
\(949\) | −3.21539 | −0.104376 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.07180 | 0.0996098 | ||||||||
\(952\) | −3.46410 | −0.112272 | ||||||||
\(953\) | −28.6410 | −0.927774 | −0.463887 | − | 0.885895i | \(-0.653546\pi\) | ||||
−0.463887 | + | 0.885895i | \(0.653546\pi\) | |||||||
\(954\) | 12.9282 | 0.418566 | ||||||||
\(955\) | −14.9282 | −0.483065 | ||||||||
\(956\) | 4.39230 | 0.142057 | ||||||||
\(957\) | −2.00000 | −0.0646508 | ||||||||
\(958\) | 13.8564 | 0.447680 | ||||||||
\(959\) | −4.53590 | −0.146472 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 17.0000 | 0.548387 | ||||||||
\(962\) | 25.8564 | 0.833644 | ||||||||
\(963\) | −6.92820 | −0.223258 | ||||||||
\(964\) | −7.07180 | −0.227767 | ||||||||
\(965\) | −11.0718 | −0.356414 | ||||||||
\(966\) | 1.46410 | 0.0471067 | ||||||||
\(967\) | −26.9282 | −0.865953 | −0.432976 | − | 0.901405i | \(-0.642537\pi\) | ||||
−0.432976 | + | 0.901405i | \(0.642537\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.8564 | 0.380686 | ||||||||
\(971\) | 35.7128 | 1.14608 | 0.573039 | − | 0.819528i | \(-0.305764\pi\) | ||||
0.573039 | + | 0.819528i | \(0.305764\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −2.92820 | −0.0938739 | ||||||||
\(974\) | 1.07180 | 0.0343426 | ||||||||
\(975\) | −3.46410 | −0.110940 | ||||||||
\(976\) | −4.92820 | −0.157748 | ||||||||
\(977\) | −37.3205 | −1.19399 | −0.596994 | − | 0.802245i | \(-0.703639\pi\) | ||||
−0.596994 | + | 0.802245i | \(0.703639\pi\) | |||||||
\(978\) | −9.46410 | −0.302629 | ||||||||
\(979\) | 3.46410 | 0.110713 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 14.3923 | 0.459511 | ||||||||
\(982\) | 1.85641 | 0.0592403 | ||||||||
\(983\) | 3.21539 | 0.102555 | 0.0512775 | − | 0.998684i | \(-0.483671\pi\) | ||||
0.0512775 | + | 0.998684i | \(0.483671\pi\) | |||||||
\(984\) | 8.92820 | 0.284621 | ||||||||
\(985\) | 18.0000 | 0.573528 | ||||||||
\(986\) | −6.92820 | −0.220639 | ||||||||
\(987\) | −6.92820 | −0.220527 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.28719 | 0.136325 | ||||||||
\(990\) | −1.00000 | −0.0317821 | ||||||||
\(991\) | −40.7846 | −1.29557 | −0.647783 | − | 0.761825i | \(-0.724304\pi\) | ||||
−0.647783 | + | 0.761825i | \(0.724304\pi\) | |||||||
\(992\) | 6.92820 | 0.219971 | ||||||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | −4.00000 | −0.126872 | ||||||||
\(995\) | 6.92820 | 0.219639 | ||||||||
\(996\) | −6.92820 | −0.219529 | ||||||||
\(997\) | 18.6795 | 0.591585 | 0.295793 | − | 0.955252i | \(-0.404416\pi\) | ||||
0.295793 | + | 0.955252i | \(0.404416\pi\) | |||||||
\(998\) | 17.0718 | 0.540398 | ||||||||
\(999\) | −7.46410 | −0.236154 |
(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 | 2310.2.a.bb.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 6930.2.a.bt.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2310.2.a.bb.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
6930.2.a.bt.1.2 | 2 | 3.2 | odd | 2 |