Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.3 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.2.c.c.199.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205i | 1.22474i | 0.790569 | + | 0.612372i | \(0.209785\pi\) | ||||
−0.790569 | + | 0.612372i | \(0.790215\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.73205 | 0.707107 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 1.46410i | 0.406069i | 0.979172 | + | 0.203034i | \(0.0650803\pi\) | ||||
−0.979172 | + | 0.203034i | \(0.934920\pi\) | |||||||
\(14\) | −3.46410 | −0.925820 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | − 1.73205i | − 0.408248i | ||||||||
\(19\) | 1.46410 | 0.335888 | 0.167944 | − | 0.985797i | \(-0.446287\pi\) | ||||
0.167944 | + | 0.985797i | \(0.446287\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | − 1.73205i | − 0.369274i | ||||||||
\(23\) | 6.92820i | 1.44463i | 0.691564 | + | 0.722315i | \(0.256922\pi\) | ||||
−0.691564 | + | 0.722315i | \(0.743078\pi\) | |||||||
\(24\) | 1.73205 | 0.353553 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.53590 | −0.497331 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 2.00000i | − 0.377964i | ||||||||
\(29\) | −3.46410 | −0.643268 | −0.321634 | − | 0.946864i | \(-0.604232\pi\) | ||||
−0.321634 | + | 0.946864i | \(0.604232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.92820 | 0.525921 | 0.262960 | − | 0.964807i | \(-0.415301\pi\) | ||||
0.262960 | + | 0.964807i | \(0.415301\pi\) | |||||||
\(32\) | − 5.19615i | − 0.918559i | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.92820i | 1.46779i | 0.679264 | + | 0.733894i | \(0.262299\pi\) | ||||
−0.679264 | + | 0.733894i | \(0.737701\pi\) | |||||||
\(38\) | 2.53590i | 0.411377i | ||||||||
\(39\) | 1.46410 | 0.234444 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.46410 | −0.541002 | −0.270501 | − | 0.962720i | \(-0.587189\pi\) | ||||
−0.270501 | + | 0.962720i | \(0.587189\pi\) | |||||||
\(42\) | 3.46410i | 0.534522i | ||||||||
\(43\) | − 8.92820i | − 1.36154i | −0.732498 | − | 0.680769i | \(-0.761646\pi\) | ||||
0.732498 | − | 0.680769i | \(-0.238354\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.0000 | −1.76930 | ||||||||
\(47\) | 6.92820i | 1.01058i | 0.862949 | + | 0.505291i | \(0.168615\pi\) | ||||
−0.862949 | + | 0.505291i | \(0.831385\pi\) | |||||||
\(48\) | 5.00000i | 0.721688i | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 1.46410i | − 0.203034i | ||||||||
\(53\) | 12.9282i | 1.77583i | 0.460012 | + | 0.887913i | \(0.347845\pi\) | ||||
−0.460012 | + | 0.887913i | \(0.652155\pi\) | |||||||
\(54\) | −1.73205 | −0.235702 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.46410 | −0.462910 | ||||||||
\(57\) | − 1.46410i | − 0.193925i | ||||||||
\(58\) | − 6.00000i | − 0.787839i | ||||||||
\(59\) | −6.92820 | −0.901975 | −0.450988 | − | 0.892530i | \(-0.648928\pi\) | ||||
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 5.07180i | 0.644119i | ||||||||
\(63\) | − 2.00000i | − 0.251976i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.73205 | −0.213201 | ||||||||
\(67\) | 8.00000i | 0.977356i | 0.872464 | + | 0.488678i | \(0.162521\pi\) | ||||
−0.872464 | + | 0.488678i | \(0.837479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.92820 | 0.834058 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.8564 | −1.64445 | −0.822226 | − | 0.569160i | \(-0.807268\pi\) | ||||
−0.822226 | + | 0.569160i | \(0.807268\pi\) | |||||||
\(72\) | − 1.73205i | − 0.204124i | ||||||||
\(73\) | − 12.3923i | − 1.45041i | −0.688533 | − | 0.725205i | \(-0.741745\pi\) | ||||
0.688533 | − | 0.725205i | \(-0.258255\pi\) | |||||||
\(74\) | −15.4641 | −1.79767 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.46410 | −0.167944 | ||||||||
\(77\) | − 2.00000i | − 0.227921i | ||||||||
\(78\) | 2.53590i | 0.287134i | ||||||||
\(79\) | 13.4641 | 1.51483 | 0.757415 | − | 0.652934i | \(-0.226462\pi\) | ||||
0.757415 | + | 0.652934i | \(0.226462\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 6.00000i | − 0.662589i | ||||||||
\(83\) | − 15.4641i | − 1.69741i | −0.528870 | − | 0.848703i | \(-0.677384\pi\) | ||||
0.528870 | − | 0.848703i | \(-0.322616\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 15.4641 | 1.66754 | ||||||||
\(87\) | 3.46410i | 0.371391i | ||||||||
\(88\) | − 1.73205i | − 0.184637i | ||||||||
\(89\) | 12.9282 | 1.37039 | 0.685193 | − | 0.728361i | \(-0.259718\pi\) | ||||
0.685193 | + | 0.728361i | \(0.259718\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.92820 | −0.306959 | ||||||||
\(92\) | − 6.92820i | − 0.722315i | ||||||||
\(93\) | − 2.92820i | − 0.303641i | ||||||||
\(94\) | −12.0000 | −1.23771 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.19615 | −0.530330 | ||||||||
\(97\) | − 10.0000i | − 1.01535i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) | ||||
0.861550 | − | 0.507673i | \(-0.169494\pi\) | |||||||
\(98\) | 5.19615i | 0.524891i | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3923 | 1.03407 | 0.517036 | − | 0.855963i | \(-0.327035\pi\) | ||||
0.517036 | + | 0.855963i | \(0.327035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 8.00000i | − 0.788263i | −0.919054 | − | 0.394132i | \(-0.871045\pi\) | ||||
0.919054 | − | 0.394132i | \(-0.128955\pi\) | |||||||
\(104\) | −2.53590 | −0.248665 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.3923 | −2.17493 | ||||||||
\(107\) | 15.4641i | 1.49497i | 0.664278 | + | 0.747486i | \(0.268739\pi\) | ||||
−0.664278 | + | 0.747486i | \(0.731261\pi\) | |||||||
\(108\) | − 1.00000i | − 0.0962250i | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.92820 | 0.847428 | ||||||||
\(112\) | − 10.0000i | − 0.944911i | ||||||||
\(113\) | − 0.928203i | − 0.0873180i | −0.999046 | − | 0.0436590i | \(-0.986098\pi\) | ||||
0.999046 | − | 0.0436590i | \(-0.0139015\pi\) | |||||||
\(114\) | 2.53590 | 0.237509 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.46410 | 0.321634 | ||||||||
\(117\) | − 1.46410i | − 0.135356i | ||||||||
\(118\) | − 12.0000i | − 1.10469i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 3.46410i | 0.313625i | ||||||||
\(123\) | 3.46410i | 0.312348i | ||||||||
\(124\) | −2.92820 | −0.262960 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.46410 | 0.308607 | ||||||||
\(127\) | − 4.92820i | − 0.437307i | −0.975803 | − | 0.218654i | \(-0.929834\pi\) | ||||
0.975803 | − | 0.218654i | \(-0.0701665\pi\) | |||||||
\(128\) | − 12.1244i | − 1.07165i | ||||||||
\(129\) | −8.92820 | −0.786084 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.07180 | 0.443125 | 0.221562 | − | 0.975146i | \(-0.428884\pi\) | ||||
0.221562 | + | 0.975146i | \(0.428884\pi\) | |||||||
\(132\) | − 1.00000i | − 0.0870388i | ||||||||
\(133\) | 2.92820i | 0.253907i | ||||||||
\(134\) | −13.8564 | −1.19701 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 18.0000i | − 1.53784i | −0.639343 | − | 0.768922i | \(-0.720793\pi\) | ||||
0.639343 | − | 0.768922i | \(-0.279207\pi\) | |||||||
\(138\) | 12.0000i | 1.02151i | ||||||||
\(139\) | 8.39230 | 0.711826 | 0.355913 | − | 0.934519i | \(-0.384170\pi\) | ||||
0.355913 | + | 0.934519i | \(0.384170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92820 | 0.583460 | ||||||||
\(142\) | − 24.0000i | − 2.01404i | ||||||||
\(143\) | − 1.46410i | − 0.122434i | ||||||||
\(144\) | 5.00000 | 0.416667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 21.4641 | 1.77638 | ||||||||
\(147\) | − 3.00000i | − 0.247436i | ||||||||
\(148\) | − 8.92820i | − 0.733894i | ||||||||
\(149\) | 8.53590 | 0.699288 | 0.349644 | − | 0.936883i | \(-0.386303\pi\) | ||||
0.349644 | + | 0.936883i | \(0.386303\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.392305 | 0.0319253 | 0.0159627 | − | 0.999873i | \(-0.494919\pi\) | ||||
0.0159627 | + | 0.999873i | \(0.494919\pi\) | |||||||
\(152\) | 2.53590i | 0.205689i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.46410 | 0.279145 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.46410 | −0.117222 | ||||||||
\(157\) | − 16.9282i | − 1.35102i | −0.737352 | − | 0.675509i | \(-0.763924\pi\) | ||||
0.737352 | − | 0.675509i | \(-0.236076\pi\) | |||||||
\(158\) | 23.3205i | 1.85528i | ||||||||
\(159\) | 12.9282 | 1.02527 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.8564 | −1.09204 | ||||||||
\(162\) | 1.73205i | 0.136083i | ||||||||
\(163\) | 17.8564i | 1.39862i | 0.714818 | + | 0.699311i | \(0.246510\pi\) | ||||
−0.714818 | + | 0.699311i | \(0.753490\pi\) | |||||||
\(164\) | 3.46410 | 0.270501 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 26.7846 | 2.07889 | ||||||||
\(167\) | 10.3923i | 0.804181i | 0.915600 | + | 0.402090i | \(0.131716\pi\) | ||||
−0.915600 | + | 0.402090i | \(0.868284\pi\) | |||||||
\(168\) | 3.46410i | 0.267261i | ||||||||
\(169\) | 10.8564 | 0.835108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.46410 | −0.111963 | ||||||||
\(172\) | 8.92820i | 0.680769i | ||||||||
\(173\) | 12.0000i | 0.912343i | 0.889892 | + | 0.456172i | \(0.150780\pi\) | ||||
−0.889892 | + | 0.456172i | \(0.849220\pi\) | |||||||
\(174\) | −6.00000 | −0.454859 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.00000 | 0.376889 | ||||||||
\(177\) | 6.92820i | 0.520756i | ||||||||
\(178\) | 22.3923i | 1.67837i | ||||||||
\(179\) | 6.92820 | 0.517838 | 0.258919 | − | 0.965899i | \(-0.416634\pi\) | ||||
0.258919 | + | 0.965899i | \(0.416634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.8564 | −0.881280 | −0.440640 | − | 0.897684i | \(-0.645248\pi\) | ||||
−0.440640 | + | 0.897684i | \(0.645248\pi\) | |||||||
\(182\) | − 5.07180i | − 0.375947i | ||||||||
\(183\) | − 2.00000i | − 0.147844i | ||||||||
\(184\) | −12.0000 | −0.884652 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.07180 | 0.371882 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − 6.92820i | − 0.505291i | ||||||||
\(189\) | −2.00000 | −0.145479 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.07180 | −0.366982 | −0.183491 | − | 0.983021i | \(-0.558740\pi\) | ||||
−0.183491 | + | 0.983021i | \(0.558740\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − 3.60770i | − 0.259688i | −0.991534 | − | 0.129844i | \(-0.958552\pi\) | ||||
0.991534 | − | 0.129844i | \(-0.0414476\pi\) | |||||||
\(194\) | 17.3205 | 1.24354 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | − 12.0000i | − 0.854965i | −0.904024 | − | 0.427482i | \(-0.859401\pi\) | ||||
0.904024 | − | 0.427482i | \(-0.140599\pi\) | |||||||
\(198\) | 1.73205i | 0.123091i | ||||||||
\(199\) | −16.7846 | −1.18983 | −0.594915 | − | 0.803789i | \(-0.702814\pi\) | ||||
−0.594915 | + | 0.803789i | \(0.702814\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 18.0000i | 1.26648i | ||||||||
\(203\) | − 6.92820i | − 0.486265i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.8564 | 0.965422 | ||||||||
\(207\) | − 6.92820i | − 0.481543i | ||||||||
\(208\) | − 7.32051i | − 0.507586i | ||||||||
\(209\) | −1.46410 | −0.101274 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.3923 | 0.853121 | 0.426561 | − | 0.904459i | \(-0.359725\pi\) | ||||
0.426561 | + | 0.904459i | \(0.359725\pi\) | |||||||
\(212\) | − 12.9282i | − 0.887913i | ||||||||
\(213\) | 13.8564i | 0.949425i | ||||||||
\(214\) | −26.7846 | −1.83096 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.73205 | −0.117851 | ||||||||
\(217\) | 5.85641i | 0.397559i | ||||||||
\(218\) | 17.3205i | 1.17309i | ||||||||
\(219\) | −12.3923 | −0.837394 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 15.4641i | 1.03788i | ||||||||
\(223\) | 17.8564i | 1.19575i | 0.801588 | + | 0.597877i | \(0.203989\pi\) | ||||
−0.801588 | + | 0.597877i | \(0.796011\pi\) | |||||||
\(224\) | 10.3923 | 0.694365 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.60770 | 0.106942 | ||||||||
\(227\) | 8.53590i | 0.566547i | 0.959039 | + | 0.283274i | \(0.0914205\pi\) | ||||
−0.959039 | + | 0.283274i | \(0.908580\pi\) | |||||||
\(228\) | 1.46410i | 0.0969625i | ||||||||
\(229\) | −3.85641 | −0.254839 | −0.127419 | − | 0.991849i | \(-0.540669\pi\) | ||||
−0.127419 | + | 0.991849i | \(0.540669\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | − 6.00000i | − 0.393919i | ||||||||
\(233\) | − 12.0000i | − 0.786146i | −0.919507 | − | 0.393073i | \(-0.871412\pi\) | ||||
0.919507 | − | 0.393073i | \(-0.128588\pi\) | |||||||
\(234\) | 2.53590 | 0.165777 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.92820 | 0.450988 | ||||||||
\(237\) | − 13.4641i | − 0.874587i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.8564 | 1.79439 | 0.897194 | − | 0.441636i | \(-0.145602\pi\) | ||||
0.897194 | + | 0.441636i | \(0.145602\pi\) | |||||||
\(242\) | 1.73205i | 0.111340i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 2.14359i | 0.136394i | ||||||||
\(248\) | 5.07180i | 0.322059i | ||||||||
\(249\) | −15.4641 | −0.979998 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.8564 | 1.63204 | 0.816021 | − | 0.578022i | \(-0.196175\pi\) | ||||
0.816021 | + | 0.578022i | \(0.196175\pi\) | |||||||
\(252\) | 2.00000i | 0.125988i | ||||||||
\(253\) | − 6.92820i | − 0.435572i | ||||||||
\(254\) | 8.53590 | 0.535590 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | 7.85641i | 0.490069i | 0.969514 | + | 0.245035i | \(0.0787993\pi\) | ||||
−0.969514 | + | 0.245035i | \(0.921201\pi\) | |||||||
\(258\) | − 15.4641i | − 0.962753i | ||||||||
\(259\) | −17.8564 | −1.10954 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.46410 | 0.214423 | ||||||||
\(262\) | 8.78461i | 0.542715i | ||||||||
\(263\) | − 27.4641i | − 1.69351i | −0.531984 | − | 0.846755i | \(-0.678553\pi\) | ||||
0.531984 | − | 0.846755i | \(-0.321447\pi\) | |||||||
\(264\) | −1.73205 | −0.106600 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.07180 | −0.310972 | ||||||||
\(267\) | − 12.9282i | − 0.791193i | ||||||||
\(268\) | − 8.00000i | − 0.488678i | ||||||||
\(269\) | 7.85641 | 0.479014 | 0.239507 | − | 0.970895i | \(-0.423014\pi\) | ||||
0.239507 | + | 0.970895i | \(0.423014\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.3923 | −1.96769 | −0.983846 | − | 0.179016i | \(-0.942709\pi\) | ||||
−0.983846 | + | 0.179016i | \(0.942709\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.92820i | 0.177223i | ||||||||
\(274\) | 31.1769 | 1.88347 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.92820 | −0.417029 | ||||||||
\(277\) | 22.5359i | 1.35405i | 0.735960 | + | 0.677025i | \(0.236731\pi\) | ||||
−0.735960 | + | 0.677025i | \(0.763269\pi\) | |||||||
\(278\) | 14.5359i | 0.871805i | ||||||||
\(279\) | −2.92820 | −0.175307 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.46410 | −0.206651 | −0.103325 | − | 0.994648i | \(-0.532948\pi\) | ||||
−0.103325 | + | 0.994648i | \(0.532948\pi\) | |||||||
\(282\) | 12.0000i | 0.714590i | ||||||||
\(283\) | − 8.92820i | − 0.530727i | −0.964148 | − | 0.265363i | \(-0.914508\pi\) | ||||
0.964148 | − | 0.265363i | \(-0.0854919\pi\) | |||||||
\(284\) | 13.8564 | 0.822226 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.53590 | 0.149951 | ||||||||
\(287\) | − 6.92820i | − 0.408959i | ||||||||
\(288\) | 5.19615i | 0.306186i | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0000 | −0.586210 | ||||||||
\(292\) | 12.3923i | 0.725205i | ||||||||
\(293\) | − 13.8564i | − 0.809500i | −0.914427 | − | 0.404750i | \(-0.867359\pi\) | ||||
0.914427 | − | 0.404750i | \(-0.132641\pi\) | |||||||
\(294\) | 5.19615 | 0.303046 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.4641 | −0.898833 | ||||||||
\(297\) | − 1.00000i | − 0.0580259i | ||||||||
\(298\) | 14.7846i | 0.856449i | ||||||||
\(299\) | −10.1436 | −0.586619 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.8564 | 1.02923 | ||||||||
\(302\) | 0.679492i | 0.0391004i | ||||||||
\(303\) | − 10.3923i | − 0.597022i | ||||||||
\(304\) | −7.32051 | −0.419860 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.0000i | 0.799022i | 0.916728 | + | 0.399511i | \(0.130820\pi\) | ||||
−0.916728 | + | 0.399511i | \(0.869180\pi\) | |||||||
\(308\) | 2.00000i | 0.113961i | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.9282 | 1.07332 | 0.536660 | − | 0.843799i | \(-0.319686\pi\) | ||||
0.536660 | + | 0.843799i | \(0.319686\pi\) | |||||||
\(312\) | 2.53590i | 0.143567i | ||||||||
\(313\) | − 7.07180i | − 0.399722i | −0.979824 | − | 0.199861i | \(-0.935951\pi\) | ||||
0.979824 | − | 0.199861i | \(-0.0640490\pi\) | |||||||
\(314\) | 29.3205 | 1.65465 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.4641 | −0.757415 | ||||||||
\(317\) | − 11.0718i | − 0.621854i | −0.950434 | − | 0.310927i | \(-0.899361\pi\) | ||||
0.950434 | − | 0.310927i | \(-0.100639\pi\) | |||||||
\(318\) | 22.3923i | 1.25570i | ||||||||
\(319\) | 3.46410 | 0.193952 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.4641 | 0.863122 | ||||||||
\(322\) | − 24.0000i | − 1.33747i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −30.9282 | −1.71295 | ||||||||
\(327\) | − 10.0000i | − 0.553001i | ||||||||
\(328\) | − 6.00000i | − 0.331295i | ||||||||
\(329\) | −13.8564 | −0.763928 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.8564 | −0.981477 | −0.490738 | − | 0.871307i | \(-0.663273\pi\) | ||||
−0.490738 | + | 0.871307i | \(0.663273\pi\) | |||||||
\(332\) | 15.4641i | 0.848703i | ||||||||
\(333\) | − 8.92820i | − 0.489263i | ||||||||
\(334\) | −18.0000 | −0.984916 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −10.0000 | −0.545545 | ||||||||
\(337\) | − 29.1769i | − 1.58937i | −0.607023 | − | 0.794684i | \(-0.707637\pi\) | ||||
0.607023 | − | 0.794684i | \(-0.292363\pi\) | |||||||
\(338\) | 18.8038i | 1.02279i | ||||||||
\(339\) | −0.928203 | −0.0504131 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.92820 | −0.158571 | ||||||||
\(342\) | − 2.53590i | − 0.137126i | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 15.4641 | 0.833768 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.7846 | −1.11739 | ||||||||
\(347\) | 1.60770i | 0.0863056i | 0.999068 | + | 0.0431528i | \(0.0137402\pi\) | ||||
−0.999068 | + | 0.0431528i | \(0.986260\pi\) | |||||||
\(348\) | − 3.46410i | − 0.185695i | ||||||||
\(349\) | 35.8564 | 1.91935 | 0.959675 | − | 0.281113i | \(-0.0907035\pi\) | ||||
0.959675 | + | 0.281113i | \(0.0907035\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.46410 | −0.0781480 | ||||||||
\(352\) | 5.19615i | 0.276956i | ||||||||
\(353\) | 0.928203i | 0.0494033i | 0.999695 | + | 0.0247016i | \(0.00786357\pi\) | ||||
−0.999695 | + | 0.0247016i | \(0.992136\pi\) | |||||||
\(354\) | −12.0000 | −0.637793 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.9282 | −0.685193 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000i | 0.634220i | ||||||||
\(359\) | −20.7846 | −1.09697 | −0.548485 | − | 0.836160i | \(-0.684795\pi\) | ||||
−0.548485 | + | 0.836160i | \(0.684795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8564 | −0.887179 | ||||||||
\(362\) | − 20.5359i | − 1.07934i | ||||||||
\(363\) | − 1.00000i | − 0.0524864i | ||||||||
\(364\) | 2.92820 | 0.153480 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.46410 | 0.181071 | ||||||||
\(367\) | 20.0000i | 1.04399i | 0.852948 | + | 0.521996i | \(0.174812\pi\) | ||||
−0.852948 | + | 0.521996i | \(0.825188\pi\) | |||||||
\(368\) | − 34.6410i | − 1.80579i | ||||||||
\(369\) | 3.46410 | 0.180334 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.8564 | −1.34240 | ||||||||
\(372\) | 2.92820i | 0.151820i | ||||||||
\(373\) | − 0.392305i | − 0.0203128i | −0.999948 | − | 0.0101564i | \(-0.996767\pi\) | ||||
0.999948 | − | 0.0101564i | \(-0.00323293\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.0000 | −0.618853 | ||||||||
\(377\) | − 5.07180i | − 0.261211i | ||||||||
\(378\) | − 3.46410i | − 0.178174i | ||||||||
\(379\) | −9.85641 | −0.506290 | −0.253145 | − | 0.967428i | \(-0.581465\pi\) | ||||
−0.253145 | + | 0.967428i | \(0.581465\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.92820 | −0.252479 | ||||||||
\(382\) | − 8.78461i | − 0.449460i | ||||||||
\(383\) | − 13.8564i | − 0.708029i | −0.935240 | − | 0.354015i | \(-0.884816\pi\) | ||||
0.935240 | − | 0.354015i | \(-0.115184\pi\) | |||||||
\(384\) | −12.1244 | −0.618718 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.24871 | 0.318051 | ||||||||
\(387\) | 8.92820i | 0.453846i | ||||||||
\(388\) | 10.0000i | 0.507673i | ||||||||
\(389\) | −24.9282 | −1.26391 | −0.631955 | − | 0.775005i | \(-0.717747\pi\) | ||||
−0.631955 | + | 0.775005i | \(0.717747\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5.19615i | 0.262445i | ||||||||
\(393\) | − 5.07180i | − 0.255838i | ||||||||
\(394\) | 20.7846 | 1.04711 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 2.00000i | 0.100377i | 0.998740 | + | 0.0501886i | \(0.0159822\pi\) | ||||
−0.998740 | + | 0.0501886i | \(0.984018\pi\) | |||||||
\(398\) | − 29.0718i | − 1.45724i | ||||||||
\(399\) | 2.92820 | 0.146594 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.8564 | 0.991582 | 0.495791 | − | 0.868442i | \(-0.334878\pi\) | ||||
0.495791 | + | 0.868442i | \(0.334878\pi\) | |||||||
\(402\) | 13.8564i | 0.691095i | ||||||||
\(403\) | 4.28719i | 0.213560i | ||||||||
\(404\) | −10.3923 | −0.517036 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | − 8.92820i | − 0.442555i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.7846 | −1.71999 | −0.859994 | − | 0.510304i | \(-0.829533\pi\) | ||||
−0.859994 | + | 0.510304i | \(0.829533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | −0.887875 | ||||||||
\(412\) | 8.00000i | 0.394132i | ||||||||
\(413\) | − 13.8564i | − 0.681829i | ||||||||
\(414\) | 12.0000 | 0.589768 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.60770 | 0.372998 | ||||||||
\(417\) | − 8.39230i | − 0.410973i | ||||||||
\(418\) | − 2.53590i | − 0.124035i | ||||||||
\(419\) | −17.0718 | −0.834012 | −0.417006 | − | 0.908904i | \(-0.636921\pi\) | ||||
−0.417006 | + | 0.908904i | \(0.636921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 21.4641i | 1.04486i | ||||||||
\(423\) | − 6.92820i | − 0.336861i | ||||||||
\(424\) | −22.3923 | −1.08747 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −24.0000 | −1.16280 | ||||||||
\(427\) | 4.00000i | 0.193574i | ||||||||
\(428\) | − 15.4641i | − 0.747486i | ||||||||
\(429\) | −1.46410 | −0.0706875 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.7846 | −1.57918 | −0.789590 | − | 0.613635i | \(-0.789706\pi\) | ||||
−0.789590 | + | 0.613635i | \(0.789706\pi\) | |||||||
\(432\) | − 5.00000i | − 0.240563i | ||||||||
\(433\) | − 27.8564i | − 1.33869i | −0.742950 | − | 0.669347i | \(-0.766574\pi\) | ||||
0.742950 | − | 0.669347i | \(-0.233426\pi\) | |||||||
\(434\) | −10.1436 | −0.486908 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | 10.1436i | 0.485234i | ||||||||
\(438\) | − 21.4641i | − 1.02559i | ||||||||
\(439\) | 29.1769 | 1.39254 | 0.696269 | − | 0.717781i | \(-0.254842\pi\) | ||||
0.696269 | + | 0.717781i | \(0.254842\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 12.0000i | − 0.570137i | −0.958507 | − | 0.285069i | \(-0.907984\pi\) | ||||
0.958507 | − | 0.285069i | \(-0.0920164\pi\) | |||||||
\(444\) | −8.92820 | −0.423714 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −30.9282 | −1.46449 | ||||||||
\(447\) | − 8.53590i | − 0.403734i | ||||||||
\(448\) | − 2.00000i | − 0.0944911i | ||||||||
\(449\) | −14.7846 | −0.697729 | −0.348864 | − | 0.937173i | \(-0.613433\pi\) | ||||
−0.348864 | + | 0.937173i | \(0.613433\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.46410 | 0.163118 | ||||||||
\(452\) | 0.928203i | 0.0436590i | ||||||||
\(453\) | − 0.392305i | − 0.0184321i | ||||||||
\(454\) | −14.7846 | −0.693876 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.53590 | 0.118754 | ||||||||
\(457\) | − 8.39230i | − 0.392575i | −0.980546 | − | 0.196288i | \(-0.937111\pi\) | ||||
0.980546 | − | 0.196288i | \(-0.0628887\pi\) | |||||||
\(458\) | − 6.67949i | − 0.312112i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.2487 | −0.570479 | −0.285240 | − | 0.958456i | \(-0.592073\pi\) | ||||
−0.285240 | + | 0.958456i | \(0.592073\pi\) | |||||||
\(462\) | − 3.46410i | − 0.161165i | ||||||||
\(463\) | 28.0000i | 1.30127i | 0.759390 | + | 0.650635i | \(0.225497\pi\) | ||||
−0.759390 | + | 0.650635i | \(0.774503\pi\) | |||||||
\(464\) | 17.3205 | 0.804084 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.7846 | 0.962828 | ||||||||
\(467\) | 18.9282i | 0.875893i | 0.899001 | + | 0.437946i | \(0.144294\pi\) | ||||
−0.899001 | + | 0.437946i | \(0.855706\pi\) | |||||||
\(468\) | 1.46410i | 0.0676781i | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.9282 | −0.780010 | ||||||||
\(472\) | − 12.0000i | − 0.552345i | ||||||||
\(473\) | 8.92820i | 0.410519i | ||||||||
\(474\) | 23.3205 | 1.07115 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 12.9282i | − 0.591942i | ||||||||
\(478\) | 20.7846i | 0.950666i | ||||||||
\(479\) | −12.0000 | −0.548294 | −0.274147 | − | 0.961688i | \(-0.588395\pi\) | ||||
−0.274147 | + | 0.961688i | \(0.588395\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.0718 | −0.596023 | ||||||||
\(482\) | 48.2487i | 2.19767i | ||||||||
\(483\) | 13.8564i | 0.630488i | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.73205 | 0.0785674 | ||||||||
\(487\) | 23.7128i | 1.07453i | 0.843413 | + | 0.537265i | \(0.180543\pi\) | ||||
−0.843413 | + | 0.537265i | \(0.819457\pi\) | |||||||
\(488\) | 3.46410i | 0.156813i | ||||||||
\(489\) | 17.8564 | 0.807495 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.0718 | −0.770439 | −0.385220 | − | 0.922825i | \(-0.625874\pi\) | ||||
−0.385220 | + | 0.922825i | \(0.625874\pi\) | |||||||
\(492\) | − 3.46410i | − 0.156174i | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −3.71281 | −0.167047 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.6410 | −0.657401 | ||||||||
\(497\) | − 27.7128i | − 1.24309i | ||||||||
\(498\) | − 26.7846i | − 1.20025i | ||||||||
\(499\) | 12.7846 | 0.572318 | 0.286159 | − | 0.958182i | \(-0.407621\pi\) | ||||
0.286159 | + | 0.958182i | \(0.407621\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.3923 | 0.464294 | ||||||||
\(502\) | 44.7846i | 1.99883i | ||||||||
\(503\) | 31.1769i | 1.39011i | 0.718957 | + | 0.695055i | \(0.244620\pi\) | ||||
−0.718957 | + | 0.695055i | \(0.755380\pi\) | |||||||
\(504\) | 3.46410 | 0.154303 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12.0000 | 0.533465 | ||||||||
\(507\) | − 10.8564i | − 0.482150i | ||||||||
\(508\) | 4.92820i | 0.218654i | ||||||||
\(509\) | 7.85641 | 0.348229 | 0.174115 | − | 0.984725i | \(-0.444294\pi\) | ||||
0.174115 | + | 0.984725i | \(0.444294\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.7846 | 1.09641 | ||||||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | 1.46410i | 0.0646417i | ||||||||
\(514\) | −13.6077 | −0.600210 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.92820 | 0.393042 | ||||||||
\(517\) | − 6.92820i | − 0.304702i | ||||||||
\(518\) | − 30.9282i | − 1.35891i | ||||||||
\(519\) | 12.0000 | 0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 6.00000i | 0.262613i | ||||||||
\(523\) | 22.0000i | 0.961993i | 0.876723 | + | 0.480996i | \(0.159725\pi\) | ||||
−0.876723 | + | 0.480996i | \(0.840275\pi\) | |||||||
\(524\) | −5.07180 | −0.221562 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 47.5692 | 2.07412 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | − 5.00000i | − 0.217597i | ||||||||
\(529\) | −25.0000 | −1.08696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.92820 | 0.300658 | ||||||||
\(532\) | − 2.92820i | − 0.126954i | ||||||||
\(533\) | − 5.07180i | − 0.219684i | ||||||||
\(534\) | 22.3923 | 0.969010 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.8564 | −0.598506 | ||||||||
\(537\) | − 6.92820i | − 0.298974i | ||||||||
\(538\) | 13.6077i | 0.586669i | ||||||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.143594 | 0.00617357 | 0.00308678 | − | 0.999995i | \(-0.499017\pi\) | ||||
0.00308678 | + | 0.999995i | \(0.499017\pi\) | |||||||
\(542\) | − 56.1051i | − 2.40992i | ||||||||
\(543\) | 11.8564i | 0.508807i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.07180 | −0.217053 | ||||||||
\(547\) | 2.00000i | 0.0855138i | 0.999086 | + | 0.0427569i | \(0.0136141\pi\) | ||||
−0.999086 | + | 0.0427569i | \(0.986386\pi\) | |||||||
\(548\) | 18.0000i | 0.768922i | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.07180 | −0.216066 | ||||||||
\(552\) | 12.0000i | 0.510754i | ||||||||
\(553\) | 26.9282i | 1.14510i | ||||||||
\(554\) | −39.0333 | −1.65837 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.39230 | −0.355913 | ||||||||
\(557\) | 44.7846i | 1.89758i | 0.315900 | + | 0.948792i | \(0.397694\pi\) | ||||
−0.315900 | + | 0.948792i | \(0.602306\pi\) | |||||||
\(558\) | − 5.07180i | − 0.214706i | ||||||||
\(559\) | 13.0718 | 0.552878 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 6.00000i | − 0.253095i | ||||||||
\(563\) | 10.3923i | 0.437983i | 0.975727 | + | 0.218992i | \(0.0702768\pi\) | ||||
−0.975727 | + | 0.218992i | \(0.929723\pi\) | |||||||
\(564\) | −6.92820 | −0.291730 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.4641 | 0.650005 | ||||||||
\(567\) | 2.00000i | 0.0839921i | ||||||||
\(568\) | − 24.0000i | − 1.00702i | ||||||||
\(569\) | 29.3205 | 1.22918 | 0.614590 | − | 0.788847i | \(-0.289322\pi\) | ||||
0.614590 | + | 0.788847i | \(0.289322\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.3923 | 1.02079 | 0.510393 | − | 0.859941i | \(-0.329500\pi\) | ||||
0.510393 | + | 0.859941i | \(0.329500\pi\) | |||||||
\(572\) | 1.46410i | 0.0612172i | ||||||||
\(573\) | 5.07180i | 0.211877i | ||||||||
\(574\) | 12.0000 | 0.500870 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 22.7846i | 0.948536i | 0.880381 | + | 0.474268i | \(0.157287\pi\) | ||||
−0.880381 | + | 0.474268i | \(0.842713\pi\) | |||||||
\(578\) | 29.4449i | 1.22474i | ||||||||
\(579\) | −3.60770 | −0.149931 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.9282 | 1.28312 | ||||||||
\(582\) | − 17.3205i | − 0.717958i | ||||||||
\(583\) | − 12.9282i | − 0.535431i | ||||||||
\(584\) | 21.4641 | 0.888191 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.0000 | 0.991431 | ||||||||
\(587\) | − 5.07180i | − 0.209335i | −0.994507 | − | 0.104668i | \(-0.966622\pi\) | ||||
0.994507 | − | 0.104668i | \(-0.0333779\pi\) | |||||||
\(588\) | 3.00000i | 0.123718i | ||||||||
\(589\) | 4.28719 | 0.176650 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.0000 | −0.493614 | ||||||||
\(592\) | − 44.6410i | − 1.83473i | ||||||||
\(593\) | 32.7846i | 1.34630i | 0.739505 | + | 0.673151i | \(0.235060\pi\) | ||||
−0.739505 | + | 0.673151i | \(0.764940\pi\) | |||||||
\(594\) | 1.73205 | 0.0710669 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.53590 | −0.349644 | ||||||||
\(597\) | 16.7846i | 0.686948i | ||||||||
\(598\) | − 17.5692i | − 0.718459i | ||||||||
\(599\) | 10.1436 | 0.414456 | 0.207228 | − | 0.978293i | \(-0.433556\pi\) | ||||
0.207228 | + | 0.978293i | \(0.433556\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.6410 | 1.49462 | 0.747309 | − | 0.664477i | \(-0.231345\pi\) | ||||
0.747309 | + | 0.664477i | \(0.231345\pi\) | |||||||
\(602\) | 30.9282i | 1.26054i | ||||||||
\(603\) | − 8.00000i | − 0.325785i | ||||||||
\(604\) | −0.392305 | −0.0159627 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.0000 | 0.731200 | ||||||||
\(607\) | 22.7846i | 0.924799i | 0.886672 | + | 0.462399i | \(0.153011\pi\) | ||||
−0.886672 | + | 0.462399i | \(0.846989\pi\) | |||||||
\(608\) | − 7.60770i | − 0.308533i | ||||||||
\(609\) | −6.92820 | −0.280745 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.1436 | −0.410366 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 0.392305i | − 0.0158450i | −0.999969 | − | 0.00792252i | \(-0.997478\pi\) | ||||
0.999969 | − | 0.00792252i | \(-0.00252184\pi\) | |||||||
\(614\) | −24.2487 | −0.978598 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.46410 | 0.139573 | ||||||||
\(617\) | − 23.0718i | − 0.928836i | −0.885616 | − | 0.464418i | \(-0.846264\pi\) | ||||
0.885616 | − | 0.464418i | \(-0.153736\pi\) | |||||||
\(618\) | − 13.8564i | − 0.557386i | ||||||||
\(619\) | −20.0000 | −0.803868 | −0.401934 | − | 0.915669i | \(-0.631662\pi\) | ||||
−0.401934 | + | 0.915669i | \(0.631662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.92820 | −0.278019 | ||||||||
\(622\) | 32.7846i | 1.31454i | ||||||||
\(623\) | 25.8564i | 1.03592i | ||||||||
\(624\) | −7.32051 | −0.293055 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.2487 | 0.489557 | ||||||||
\(627\) | 1.46410i | 0.0584706i | ||||||||
\(628\) | 16.9282i | 0.675509i | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.9282 | −1.39047 | −0.695235 | − | 0.718783i | \(-0.744700\pi\) | ||||
−0.695235 | + | 0.718783i | \(0.744700\pi\) | |||||||
\(632\) | 23.3205i | 0.927640i | ||||||||
\(633\) | − 12.3923i | − 0.492550i | ||||||||
\(634\) | 19.1769 | 0.761613 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.9282 | −0.512637 | ||||||||
\(637\) | 4.39230i | 0.174029i | ||||||||
\(638\) | 6.00000i | 0.237542i | ||||||||
\(639\) | 13.8564 | 0.548151 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.928203 | 0.0366618 | 0.0183309 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183309 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(642\) | 26.7846i | 1.05710i | ||||||||
\(643\) | 45.5692i | 1.79707i | 0.438897 | + | 0.898537i | \(0.355369\pi\) | ||||
−0.438897 | + | 0.898537i | \(0.644631\pi\) | |||||||
\(644\) | 13.8564 | 0.546019 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 27.7128i | − 1.08950i | −0.838597 | − | 0.544752i | \(-0.816624\pi\) | ||||
0.838597 | − | 0.544752i | \(-0.183376\pi\) | |||||||
\(648\) | 1.73205i | 0.0680414i | ||||||||
\(649\) | 6.92820 | 0.271956 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.85641 | 0.229531 | ||||||||
\(652\) | − 17.8564i | − 0.699311i | ||||||||
\(653\) | 7.85641i | 0.307445i | 0.988114 | + | 0.153722i | \(0.0491262\pi\) | ||||
−0.988114 | + | 0.153722i | \(0.950874\pi\) | |||||||
\(654\) | 17.3205 | 0.677285 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 17.3205 | 0.676252 | ||||||||
\(657\) | 12.3923i | 0.483470i | ||||||||
\(658\) | − 24.0000i | − 0.935617i | ||||||||
\(659\) | −39.7128 | −1.54699 | −0.773496 | − | 0.633801i | \(-0.781494\pi\) | ||||
−0.773496 | + | 0.633801i | \(0.781494\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(662\) | − 30.9282i | − 1.20206i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.7846 | 1.03944 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.4641 | 0.599222 | ||||||||
\(667\) | − 24.0000i | − 0.929284i | ||||||||
\(668\) | − 10.3923i | − 0.402090i | ||||||||
\(669\) | 17.8564 | 0.690369 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | − 10.3923i | − 0.400892i | ||||||||
\(673\) | − 31.3205i | − 1.20732i | −0.797243 | − | 0.603658i | \(-0.793709\pi\) | ||||
0.797243 | − | 0.603658i | \(-0.206291\pi\) | |||||||
\(674\) | 50.5359 | 1.94657 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.8564 | −0.417554 | ||||||||
\(677\) | − 32.7846i | − 1.26001i | −0.776589 | − | 0.630007i | \(-0.783052\pi\) | ||||
0.776589 | − | 0.630007i | \(-0.216948\pi\) | |||||||
\(678\) | − 1.60770i | − 0.0617432i | ||||||||
\(679\) | 20.0000 | 0.767530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.53590 | 0.327096 | ||||||||
\(682\) | − 5.07180i | − 0.194209i | ||||||||
\(683\) | − 8.78461i | − 0.336134i | −0.985776 | − | 0.168067i | \(-0.946248\pi\) | ||||
0.985776 | − | 0.168067i | \(-0.0537525\pi\) | |||||||
\(684\) | 1.46410 | 0.0559813 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −34.6410 | −1.32260 | ||||||||
\(687\) | 3.85641i | 0.147131i | ||||||||
\(688\) | 44.6410i | 1.70192i | ||||||||
\(689\) | −18.9282 | −0.721107 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.71281 | −0.293409 | −0.146705 | − | 0.989180i | \(-0.546867\pi\) | ||||
−0.146705 | + | 0.989180i | \(0.546867\pi\) | |||||||
\(692\) | − 12.0000i | − 0.456172i | ||||||||
\(693\) | 2.00000i | 0.0759737i | ||||||||
\(694\) | −2.78461 | −0.105702 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.00000 | −0.227429 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 62.1051i | 2.35071i | ||||||||
\(699\) | −12.0000 | −0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.5359 | 1.22886 | 0.614432 | − | 0.788970i | \(-0.289385\pi\) | ||||
0.614432 | + | 0.788970i | \(0.289385\pi\) | |||||||
\(702\) | − 2.53590i | − 0.0957113i | ||||||||
\(703\) | 13.0718i | 0.493012i | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.60770 | −0.0605064 | ||||||||
\(707\) | 20.7846i | 0.781686i | ||||||||
\(708\) | − 6.92820i | − 0.260378i | ||||||||
\(709\) | −15.8564 | −0.595500 | −0.297750 | − | 0.954644i | \(-0.596236\pi\) | ||||
−0.297750 | + | 0.954644i | \(0.596236\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.4641 | −0.504943 | ||||||||
\(712\) | 22.3923i | 0.839187i | ||||||||
\(713\) | 20.2872i | 0.759761i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.92820 | −0.258919 | ||||||||
\(717\) | − 12.0000i | − 0.448148i | ||||||||
\(718\) | − 36.0000i | − 1.34351i | ||||||||
\(719\) | 18.9282 | 0.705903 | 0.352951 | − | 0.935642i | \(-0.385178\pi\) | ||||
0.352951 | + | 0.935642i | \(0.385178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | − 29.1962i | − 1.08657i | ||||||||
\(723\) | − 27.8564i | − 1.03599i | ||||||||
\(724\) | 11.8564 | 0.440640 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.73205 | 0.0642824 | ||||||||
\(727\) | 8.00000i | 0.296704i | 0.988935 | + | 0.148352i | \(0.0473968\pi\) | ||||
−0.988935 | + | 0.148352i | \(0.952603\pi\) | |||||||
\(728\) | − 5.07180i | − 0.187973i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.00000i | 0.0739221i | ||||||||
\(733\) | 49.9615i | 1.84537i | 0.385553 | + | 0.922686i | \(0.374011\pi\) | ||||
−0.385553 | + | 0.922686i | \(0.625989\pi\) | |||||||
\(734\) | −34.6410 | −1.27862 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.0000 | 1.32698 | ||||||||
\(737\) | − 8.00000i | − 0.294684i | ||||||||
\(738\) | 6.00000i | 0.220863i | ||||||||
\(739\) | −10.5359 | −0.387569 | −0.193785 | − | 0.981044i | \(-0.562076\pi\) | ||||
−0.193785 | + | 0.981044i | \(0.562076\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.14359 | 0.0787469 | ||||||||
\(742\) | − 44.7846i | − 1.64409i | ||||||||
\(743\) | − 46.3923i | − 1.70197i | −0.525191 | − | 0.850984i | \(-0.676006\pi\) | ||||
0.525191 | − | 0.850984i | \(-0.323994\pi\) | |||||||
\(744\) | 5.07180 | 0.185941 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.679492 | 0.0248780 | ||||||||
\(747\) | 15.4641i | 0.565802i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.9282 | −1.13009 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0718 | 0.476997 | 0.238498 | − | 0.971143i | \(-0.423345\pi\) | ||||
0.238498 | + | 0.971143i | \(0.423345\pi\) | |||||||
\(752\) | − 34.6410i | − 1.26323i | ||||||||
\(753\) | − 25.8564i | − 0.942260i | ||||||||
\(754\) | 8.78461 | 0.319917 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.00000 | 0.0727393 | ||||||||
\(757\) | − 6.78461i | − 0.246591i | −0.992370 | − | 0.123295i | \(-0.960654\pi\) | ||||
0.992370 | − | 0.123295i | \(-0.0393463\pi\) | |||||||
\(758\) | − 17.0718i | − 0.620076i | ||||||||
\(759\) | −6.92820 | −0.251478 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.4641 | −1.43057 | −0.715286 | − | 0.698832i | \(-0.753704\pi\) | ||||
−0.715286 | + | 0.698832i | \(0.753704\pi\) | |||||||
\(762\) | − 8.53590i | − 0.309223i | ||||||||
\(763\) | 20.0000i | 0.724049i | ||||||||
\(764\) | 5.07180 | 0.183491 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | − 10.1436i | − 0.366264i | ||||||||
\(768\) | − 19.0000i | − 0.685603i | ||||||||
\(769\) | 46.4974 | 1.67674 | 0.838370 | − | 0.545102i | \(-0.183509\pi\) | ||||
0.838370 | + | 0.545102i | \(0.183509\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.85641 | 0.282942 | ||||||||
\(772\) | 3.60770i | 0.129844i | ||||||||
\(773\) | 31.8564i | 1.14580i | 0.819627 | + | 0.572898i | \(0.194181\pi\) | ||||
−0.819627 | + | 0.572898i | \(0.805819\pi\) | |||||||
\(774\) | −15.4641 | −0.555846 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.3205 | 0.621770 | ||||||||
\(777\) | 17.8564i | 0.640595i | ||||||||
\(778\) | − 43.1769i | − 1.54797i | ||||||||
\(779\) | −5.07180 | −0.181716 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8564 | 0.495821 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 3.46410i | − 0.123797i | ||||||||
\(784\) | −15.0000 | −0.535714 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.78461 | 0.313337 | ||||||||
\(787\) | − 18.7846i | − 0.669599i | −0.942289 | − | 0.334800i | \(-0.891331\pi\) | ||||
0.942289 | − | 0.334800i | \(-0.108669\pi\) | |||||||
\(788\) | 12.0000i | 0.427482i | ||||||||
\(789\) | −27.4641 | −0.977748 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.85641 | 0.0660062 | ||||||||
\(792\) | 1.73205i | 0.0615457i | ||||||||
\(793\) | 2.92820i | 0.103984i | ||||||||
\(794\) | −3.46410 | −0.122936 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.7846 | 0.594915 | ||||||||
\(797\) | 16.6410i | 0.589455i | 0.955581 | + | 0.294728i | \(0.0952289\pi\) | ||||
−0.955581 | + | 0.294728i | \(0.904771\pi\) | |||||||
\(798\) | 5.07180i | 0.179540i | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.9282 | −0.456796 | ||||||||
\(802\) | 34.3923i | 1.21443i | ||||||||
\(803\) | 12.3923i | 0.437315i | ||||||||
\(804\) | −8.00000 | −0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.42563 | −0.261557 | ||||||||
\(807\) | − 7.85641i | − 0.276559i | ||||||||
\(808\) | 18.0000i | 0.633238i | ||||||||
\(809\) | 8.53590 | 0.300106 | 0.150053 | − | 0.988678i | \(-0.452056\pi\) | ||||
0.150053 | + | 0.988678i | \(0.452056\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.39230 | −0.294694 | −0.147347 | − | 0.989085i | \(-0.547073\pi\) | ||||
−0.147347 | + | 0.989085i | \(0.547073\pi\) | |||||||
\(812\) | 6.92820i | 0.243132i | ||||||||
\(813\) | 32.3923i | 1.13605i | ||||||||
\(814\) | 15.4641 | 0.542016 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 13.0718i | − 0.457324i | ||||||||
\(818\) | − 60.2487i | − 2.10655i | ||||||||
\(819\) | 2.92820 | 0.102320 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.4641 | 0.958504 | 0.479252 | − | 0.877677i | \(-0.340908\pi\) | ||||
0.479252 | + | 0.877677i | \(0.340908\pi\) | |||||||
\(822\) | − 31.1769i | − 1.08742i | ||||||||
\(823\) | − 49.5692i | − 1.72787i | −0.503600 | − | 0.863937i | \(-0.667991\pi\) | ||||
0.503600 | − | 0.863937i | \(-0.332009\pi\) | |||||||
\(824\) | 13.8564 | 0.482711 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.0000 | 0.835067 | ||||||||
\(827\) | 1.60770i | 0.0559050i | 0.999609 | + | 0.0279525i | \(0.00889872\pi\) | ||||
−0.999609 | + | 0.0279525i | \(0.991101\pi\) | |||||||
\(828\) | 6.92820i | 0.240772i | ||||||||
\(829\) | 25.7128 | 0.893043 | 0.446521 | − | 0.894773i | \(-0.352663\pi\) | ||||
0.446521 | + | 0.894773i | \(0.352663\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.5359 | 0.781762 | ||||||||
\(832\) | − 1.46410i | − 0.0507586i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.5359 | 0.503337 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.46410 | 0.0506370 | ||||||||
\(837\) | 2.92820i | 0.101214i | ||||||||
\(838\) | − 29.5692i | − 1.02145i | ||||||||
\(839\) | −15.2154 | −0.525294 | −0.262647 | − | 0.964892i | \(-0.584595\pi\) | ||||
−0.262647 | + | 0.964892i | \(0.584595\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.0000 | −0.586207 | ||||||||
\(842\) | 3.46410i | 0.119381i | ||||||||
\(843\) | 3.46410i | 0.119310i | ||||||||
\(844\) | −12.3923 | −0.426561 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.0000 | 0.412568 | ||||||||
\(847\) | 2.00000i | 0.0687208i | ||||||||
\(848\) | − 64.6410i | − 2.21978i | ||||||||
\(849\) | −8.92820 | −0.306415 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −61.8564 | −2.12041 | ||||||||
\(852\) | − 13.8564i | − 0.474713i | ||||||||
\(853\) | − 24.3923i | − 0.835177i | −0.908636 | − | 0.417588i | \(-0.862875\pi\) | ||||
0.908636 | − | 0.417588i | \(-0.137125\pi\) | |||||||
\(854\) | −6.92820 | −0.237078 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.7846 | −0.915479 | ||||||||
\(857\) | − 10.1436i | − 0.346499i | −0.984878 | − | 0.173249i | \(-0.944573\pi\) | ||||
0.984878 | − | 0.173249i | \(-0.0554266\pi\) | |||||||
\(858\) | − 2.53590i | − 0.0865741i | ||||||||
\(859\) | −47.7128 | −1.62794 | −0.813970 | − | 0.580907i | \(-0.802698\pi\) | ||||
−0.813970 | + | 0.580907i | \(0.802698\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.92820 | −0.236113 | ||||||||
\(862\) | − 56.7846i | − 1.93409i | ||||||||
\(863\) | 10.1436i | 0.345292i | 0.984984 | + | 0.172646i | \(0.0552317\pi\) | ||||
−0.984984 | + | 0.172646i | \(0.944768\pi\) | |||||||
\(864\) | 5.19615 | 0.176777 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 48.2487 | 1.63956 | ||||||||
\(867\) | − 17.0000i | − 0.577350i | ||||||||
\(868\) | − 5.85641i | − 0.198779i | ||||||||
\(869\) | −13.4641 | −0.456738 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.7128 | −0.396874 | ||||||||
\(872\) | 17.3205i | 0.586546i | ||||||||
\(873\) | 10.0000i | 0.338449i | ||||||||
\(874\) | −17.5692 | −0.594288 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.3923 | 0.418697 | ||||||||
\(877\) | 14.2487i | 0.481145i | 0.970631 | + | 0.240572i | \(0.0773351\pi\) | ||||
−0.970631 | + | 0.240572i | \(0.922665\pi\) | |||||||
\(878\) | 50.5359i | 1.70550i | ||||||||
\(879\) | −13.8564 | −0.467365 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.9282 | 0.435562 | 0.217781 | − | 0.975998i | \(-0.430118\pi\) | ||||
0.217781 | + | 0.975998i | \(0.430118\pi\) | |||||||
\(882\) | − 5.19615i | − 0.174964i | ||||||||
\(883\) | 4.00000i | 0.134611i | 0.997732 | + | 0.0673054i | \(0.0214402\pi\) | ||||
−0.997732 | + | 0.0673054i | \(0.978560\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.7846 | 0.698273 | ||||||||
\(887\) | − 36.2487i | − 1.21711i | −0.793511 | − | 0.608556i | \(-0.791749\pi\) | ||||
0.793511 | − | 0.608556i | \(-0.208251\pi\) | |||||||
\(888\) | 15.4641i | 0.518941i | ||||||||
\(889\) | 9.85641 | 0.330573 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | − 17.8564i | − 0.597877i | ||||||||
\(893\) | 10.1436i | 0.339442i | ||||||||
\(894\) | 14.7846 | 0.494471 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 24.2487 | 0.810093 | ||||||||
\(897\) | 10.1436i | 0.338685i | ||||||||
\(898\) | − 25.6077i | − 0.854540i | ||||||||
\(899\) | −10.1436 | −0.338308 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 6.00000i | 0.199778i | ||||||||
\(903\) | − 17.8564i | − 0.594224i | ||||||||
\(904\) | 1.60770 | 0.0534711 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.679492 | 0.0225746 | ||||||||
\(907\) | 45.8564i | 1.52264i | 0.648378 | + | 0.761318i | \(0.275448\pi\) | ||||
−0.648378 | + | 0.761318i | \(0.724552\pi\) | |||||||
\(908\) | − 8.53590i | − 0.283274i | ||||||||
\(909\) | −10.3923 | −0.344691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.07180 | 0.168036 | 0.0840181 | − | 0.996464i | \(-0.473225\pi\) | ||||
0.0840181 | + | 0.996464i | \(0.473225\pi\) | |||||||
\(912\) | 7.32051i | 0.242406i | ||||||||
\(913\) | 15.4641i | 0.511787i | ||||||||
\(914\) | 14.5359 | 0.480805 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.85641 | 0.127419 | ||||||||
\(917\) | 10.1436i | 0.334971i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.6077 | 0.382903 | 0.191451 | − | 0.981502i | \(-0.438681\pi\) | ||||
0.191451 | + | 0.981502i | \(0.438681\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | 0.461316 | ||||||||
\(922\) | − 21.2154i | − 0.698692i | ||||||||
\(923\) | − 20.2872i | − 0.667761i | ||||||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −48.4974 | −1.59372 | ||||||||
\(927\) | 8.00000i | 0.262754i | ||||||||
\(928\) | 18.0000i | 0.590879i | ||||||||
\(929\) | 38.7846 | 1.27248 | 0.636241 | − | 0.771490i | \(-0.280488\pi\) | ||||
0.636241 | + | 0.771490i | \(0.280488\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.39230 | 0.143952 | ||||||||
\(932\) | 12.0000i | 0.393073i | ||||||||
\(933\) | − 18.9282i | − 0.619682i | ||||||||
\(934\) | −32.7846 | −1.07275 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.53590 | 0.0828884 | ||||||||
\(937\) | 0.392305i | 0.0128160i | 0.999979 | + | 0.00640802i | \(0.00203975\pi\) | ||||
−0.999979 | + | 0.00640802i | \(0.997960\pi\) | |||||||
\(938\) | − 27.7128i | − 0.904855i | ||||||||
\(939\) | −7.07180 | −0.230779 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.5359 | 0.669451 | 0.334726 | − | 0.942316i | \(-0.391356\pi\) | ||||
0.334726 | + | 0.942316i | \(0.391356\pi\) | |||||||
\(942\) | − 29.3205i | − 0.955314i | ||||||||
\(943\) | − 24.0000i | − 0.781548i | ||||||||
\(944\) | 34.6410 | 1.12747 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.4641 | −0.502781 | ||||||||
\(947\) | − 5.07180i | − 0.164811i | −0.996599 | − | 0.0824056i | \(-0.973740\pi\) | ||||
0.996599 | − | 0.0824056i | \(-0.0262603\pi\) | |||||||
\(948\) | 13.4641i | 0.437294i | ||||||||
\(949\) | 18.1436 | 0.588966 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.0718 | −0.359028 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.7846i | 1.45072i | 0.688372 | + | 0.725358i | \(0.258326\pi\) | ||||
−0.688372 | + | 0.725358i | \(0.741674\pi\) | |||||||
\(954\) | 22.3923 | 0.724978 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.0000 | −0.388108 | ||||||||
\(957\) | − 3.46410i | − 0.111979i | ||||||||
\(958\) | − 20.7846i | − 0.671520i | ||||||||
\(959\) | 36.0000 | 1.16250 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.4256 | −0.723407 | ||||||||
\(962\) | − 22.6410i | − 0.729976i | ||||||||
\(963\) | − 15.4641i | − 0.498324i | ||||||||
\(964\) | −27.8564 | −0.897194 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −24.0000 | −0.772187 | ||||||||
\(967\) | − 18.7846i | − 0.604072i | −0.953296 | − | 0.302036i | \(-0.902334\pi\) | ||||
0.953296 | − | 0.302036i | \(-0.0976663\pi\) | |||||||
\(968\) | 1.73205i | 0.0556702i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.85641 | −0.0595749 | −0.0297875 | − | 0.999556i | \(-0.509483\pi\) | ||||
−0.0297875 | + | 0.999556i | \(0.509483\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 16.7846i | 0.538090i | ||||||||
\(974\) | −41.0718 | −1.31603 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0000 | −0.320092 | ||||||||
\(977\) | − 35.5692i | − 1.13796i | −0.822351 | − | 0.568980i | \(-0.807338\pi\) | ||||
0.822351 | − | 0.568980i | \(-0.192662\pi\) | |||||||
\(978\) | 30.9282i | 0.988975i | ||||||||
\(979\) | −12.9282 | −0.413187 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | − 29.5692i | − 0.943592i | ||||||||
\(983\) | − 24.0000i | − 0.765481i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(984\) | −6.00000 | −0.191273 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.8564i | 0.441054i | ||||||||
\(988\) | − 2.14359i | − 0.0681968i | ||||||||
\(989\) | 61.8564 | 1.96692 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.7846 | −1.54969 | −0.774847 | − | 0.632149i | \(-0.782173\pi\) | ||||
−0.774847 | + | 0.632149i | \(0.782173\pi\) | |||||||
\(992\) | − 15.2154i | − 0.483089i | ||||||||
\(993\) | 17.8564i | 0.566656i | ||||||||
\(994\) | 48.0000 | 1.52247 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15.4641 | 0.489999 | ||||||||
\(997\) | 48.3923i | 1.53260i | 0.642483 | + | 0.766300i | \(0.277904\pi\) | ||||
−0.642483 | + | 0.766300i | \(0.722096\pi\) | |||||||
\(998\) | 22.1436i | 0.700943i | ||||||||
\(999\) | −8.92820 | −0.282476 |
(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 | 825.2.c.c.199.3 | 4 | ||
3.2 | odd | 2 | 2475.2.c.n.199.2 | 4 | |||
5.2 | odd | 4 | 825.2.a.e.1.1 | 2 | |||
5.3 | odd | 4 | 165.2.a.b.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 825.2.c.c.199.2 | 4 | ||
15.2 | even | 4 | 2475.2.a.r.1.2 | 2 | |||
15.8 | even | 4 | 495.2.a.c.1.1 | 2 | |||
15.14 | odd | 2 | 2475.2.c.n.199.3 | 4 | |||
20.3 | even | 4 | 2640.2.a.x.1.1 | 2 | |||
35.13 | even | 4 | 8085.2.a.bd.1.2 | 2 | |||
55.32 | even | 4 | 9075.2.a.bh.1.2 | 2 | |||
55.43 | even | 4 | 1815.2.a.i.1.1 | 2 | |||
60.23 | odd | 4 | 7920.2.a.bz.1.1 | 2 | |||
165.98 | odd | 4 | 5445.2.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.b.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
495.2.a.c.1.1 | 2 | 15.8 | even | 4 | |||
825.2.a.e.1.1 | 2 | 5.2 | odd | 4 | |||
825.2.c.c.199.2 | 4 | 5.4 | even | 2 | inner | ||
825.2.c.c.199.3 | 4 | 1.1 | even | 1 | trivial | ||
1815.2.a.i.1.1 | 2 | 55.43 | even | 4 | |||
2475.2.a.r.1.2 | 2 | 15.2 | even | 4 | |||
2475.2.c.n.199.2 | 4 | 3.2 | odd | 2 | |||
2475.2.c.n.199.3 | 4 | 15.14 | odd | 2 | |||
2640.2.a.x.1.1 | 2 | 20.3 | even | 4 | |||
5445.2.a.s.1.2 | 2 | 165.98 | odd | 4 | |||
7920.2.a.bz.1.1 | 2 | 60.23 | odd | 4 | |||
8085.2.a.bd.1.2 | 2 | 35.13 | even | 4 | |||
9075.2.a.bh.1.2 | 2 | 55.32 | even | 4 |