Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7935,2,Mod(1,7935)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7935, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7935.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7935 = 3 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7935.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.3612940039\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 345) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7935.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44949 | 1.73205 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 2.00000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.44949 | 1.00000 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 4.89898 | 1.73205 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.44949 | 0.774597 | ||||||||
\(11\) | 2.44949 | 0.738549 | 0.369274 | − | 0.929320i | \(-0.379606\pi\) | ||||
0.369274 | + | 0.929320i | \(0.379606\pi\) | |||||||
\(12\) | 4.00000 | 1.15470 | ||||||||
\(13\) | −0.449490 | −0.124666 | −0.0623330 | − | 0.998055i | \(-0.519854\pi\) | ||||
−0.0623330 | + | 0.998055i | \(0.519854\pi\) | |||||||
\(14\) | 2.44949 | 0.654654 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 0.550510 | 0.133518 | 0.0667592 | − | 0.997769i | \(-0.478734\pi\) | ||||
0.0667592 | + | 0.997769i | \(0.478734\pi\) | |||||||
\(18\) | 2.44949 | 0.577350 | ||||||||
\(19\) | 0.449490 | 0.103120 | 0.0515600 | − | 0.998670i | \(-0.483581\pi\) | ||||
0.0515600 | + | 0.998670i | \(0.483581\pi\) | |||||||
\(20\) | 4.00000 | 0.894427 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 6.00000 | 1.27920 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 4.89898 | 1.00000 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.10102 | −0.215928 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | −4.34847 | −0.807490 | −0.403745 | − | 0.914871i | \(-0.632292\pi\) | ||||
−0.403745 | + | 0.914871i | \(0.632292\pi\) | |||||||
\(30\) | 2.44949 | 0.447214 | ||||||||
\(31\) | 9.89898 | 1.77791 | 0.888955 | − | 0.457995i | \(-0.151432\pi\) | ||||
0.888955 | + | 0.457995i | \(0.151432\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.44949 | 0.426401 | ||||||||
\(34\) | 1.34847 | 0.231261 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 4.00000 | 0.666667 | ||||||||
\(37\) | 5.89898 | 0.969786 | 0.484893 | − | 0.874573i | \(-0.338858\pi\) | ||||
0.484893 | + | 0.874573i | \(0.338858\pi\) | |||||||
\(38\) | 1.10102 | 0.178609 | ||||||||
\(39\) | −0.449490 | −0.0719760 | ||||||||
\(40\) | 4.89898 | 0.774597 | ||||||||
\(41\) | 0.550510 | 0.0859753 | 0.0429876 | − | 0.999076i | \(-0.486312\pi\) | ||||
0.0429876 | + | 0.999076i | \(0.486312\pi\) | |||||||
\(42\) | 2.44949 | 0.377964 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 9.79796 | 1.47710 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.55051 | 0.517895 | 0.258948 | − | 0.965891i | \(-0.416624\pi\) | ||||
0.258948 | + | 0.965891i | \(0.416624\pi\) | |||||||
\(48\) | 4.00000 | 0.577350 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 2.44949 | 0.346410 | ||||||||
\(51\) | 0.550510 | 0.0770869 | ||||||||
\(52\) | −1.79796 | −0.249332 | ||||||||
\(53\) | −5.44949 | −0.748545 | −0.374272 | − | 0.927319i | \(-0.622108\pi\) | ||||
−0.374272 | + | 0.927319i | \(0.622108\pi\) | |||||||
\(54\) | 2.44949 | 0.333333 | ||||||||
\(55\) | 2.44949 | 0.330289 | ||||||||
\(56\) | 4.89898 | 0.654654 | ||||||||
\(57\) | 0.449490 | 0.0595364 | ||||||||
\(58\) | −10.6515 | −1.39861 | ||||||||
\(59\) | −4.34847 | −0.566122 | −0.283061 | − | 0.959102i | \(-0.591350\pi\) | ||||
−0.283061 | + | 0.959102i | \(0.591350\pi\) | |||||||
\(60\) | 4.00000 | 0.516398 | ||||||||
\(61\) | −15.3485 | −1.96517 | −0.982585 | − | 0.185813i | \(-0.940508\pi\) | ||||
−0.982585 | + | 0.185813i | \(0.940508\pi\) | |||||||
\(62\) | 24.2474 | 3.07943 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −0.449490 | −0.0557523 | ||||||||
\(66\) | 6.00000 | 0.738549 | ||||||||
\(67\) | 7.00000 | 0.855186 | 0.427593 | − | 0.903971i | \(-0.359362\pi\) | ||||
0.427593 | + | 0.903971i | \(0.359362\pi\) | |||||||
\(68\) | 2.20204 | 0.267037 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.44949 | 0.292770 | ||||||||
\(71\) | 10.3485 | 1.22814 | 0.614069 | − | 0.789253i | \(-0.289532\pi\) | ||||
0.614069 | + | 0.789253i | \(0.289532\pi\) | |||||||
\(72\) | 4.89898 | 0.577350 | ||||||||
\(73\) | 9.34847 | 1.09416 | 0.547078 | − | 0.837082i | \(-0.315740\pi\) | ||||
0.547078 | + | 0.837082i | \(0.315740\pi\) | |||||||
\(74\) | 14.4495 | 1.67972 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 1.79796 | 0.206240 | ||||||||
\(77\) | 2.44949 | 0.279145 | ||||||||
\(78\) | −1.10102 | −0.124666 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 4.00000 | 0.447214 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.34847 | 0.148914 | ||||||||
\(83\) | 9.24745 | 1.01504 | 0.507520 | − | 0.861640i | \(-0.330562\pi\) | ||||
0.507520 | + | 0.861640i | \(0.330562\pi\) | |||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | 0.550510 | 0.0597112 | ||||||||
\(86\) | −4.89898 | −0.528271 | ||||||||
\(87\) | −4.34847 | −0.466205 | ||||||||
\(88\) | 12.0000 | 1.27920 | ||||||||
\(89\) | 7.10102 | 0.752707 | 0.376353 | − | 0.926476i | \(-0.377178\pi\) | ||||
0.376353 | + | 0.926476i | \(0.377178\pi\) | |||||||
\(90\) | 2.44949 | 0.258199 | ||||||||
\(91\) | −0.449490 | −0.0471193 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.89898 | 1.02648 | ||||||||
\(94\) | 8.69694 | 0.897021 | ||||||||
\(95\) | 0.449490 | 0.0461167 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.8990 | −1.30969 | −0.654846 | − | 0.755762i | \(-0.727267\pi\) | ||||
−0.654846 | + | 0.755762i | \(0.727267\pi\) | |||||||
\(98\) | −14.6969 | −1.48461 | ||||||||
\(99\) | 2.44949 | 0.246183 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | −17.4495 | −1.73629 | −0.868145 | − | 0.496311i | \(-0.834687\pi\) | ||||
−0.868145 | + | 0.496311i | \(0.834687\pi\) | |||||||
\(102\) | 1.34847 | 0.133518 | ||||||||
\(103\) | −16.6969 | −1.64520 | −0.822599 | − | 0.568622i | \(-0.807477\pi\) | ||||
−0.822599 | + | 0.568622i | \(0.807477\pi\) | |||||||
\(104\) | −2.20204 | −0.215928 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | −13.3485 | −1.29652 | ||||||||
\(107\) | 0.550510 | 0.0532198 | 0.0266099 | − | 0.999646i | \(-0.491529\pi\) | ||||
0.0266099 | + | 0.999646i | \(0.491529\pi\) | |||||||
\(108\) | 4.00000 | 0.384900 | ||||||||
\(109\) | −16.4495 | −1.57558 | −0.787788 | − | 0.615947i | \(-0.788774\pi\) | ||||
−0.787788 | + | 0.615947i | \(0.788774\pi\) | |||||||
\(110\) | 6.00000 | 0.572078 | ||||||||
\(111\) | 5.89898 | 0.559906 | ||||||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | 16.3485 | 1.53793 | 0.768967 | − | 0.639288i | \(-0.220771\pi\) | ||||
0.768967 | + | 0.639288i | \(0.220771\pi\) | |||||||
\(114\) | 1.10102 | 0.103120 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −17.3939 | −1.61498 | ||||||||
\(117\) | −0.449490 | −0.0415553 | ||||||||
\(118\) | −10.6515 | −0.980553 | ||||||||
\(119\) | 0.550510 | 0.0504652 | ||||||||
\(120\) | 4.89898 | 0.447214 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | −37.5959 | −3.40377 | ||||||||
\(123\) | 0.550510 | 0.0496378 | ||||||||
\(124\) | 39.5959 | 3.55582 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.44949 | 0.218218 | ||||||||
\(127\) | −6.44949 | −0.572300 | −0.286150 | − | 0.958185i | \(-0.592376\pi\) | ||||
−0.286150 | + | 0.958185i | \(0.592376\pi\) | |||||||
\(128\) | −19.5959 | −1.73205 | ||||||||
\(129\) | −2.00000 | −0.176090 | ||||||||
\(130\) | −1.10102 | −0.0965659 | ||||||||
\(131\) | 19.5959 | 1.71210 | 0.856052 | − | 0.516890i | \(-0.172910\pi\) | ||||
0.856052 | + | 0.516890i | \(0.172910\pi\) | |||||||
\(132\) | 9.79796 | 0.852803 | ||||||||
\(133\) | 0.449490 | 0.0389757 | ||||||||
\(134\) | 17.1464 | 1.48123 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 2.69694 | 0.231261 | ||||||||
\(137\) | 7.10102 | 0.606681 | 0.303341 | − | 0.952882i | \(-0.401898\pi\) | ||||
0.303341 | + | 0.952882i | \(0.401898\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.7980 | 1.25515 | 0.627573 | − | 0.778558i | \(-0.284048\pi\) | ||||
0.627573 | + | 0.778558i | \(0.284048\pi\) | |||||||
\(140\) | 4.00000 | 0.338062 | ||||||||
\(141\) | 3.55051 | 0.299007 | ||||||||
\(142\) | 25.3485 | 2.12720 | ||||||||
\(143\) | −1.10102 | −0.0920720 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | −4.34847 | −0.361121 | ||||||||
\(146\) | 22.8990 | 1.89513 | ||||||||
\(147\) | −6.00000 | −0.494872 | ||||||||
\(148\) | 23.5959 | 1.93957 | ||||||||
\(149\) | −13.3485 | −1.09355 | −0.546775 | − | 0.837280i | \(-0.684145\pi\) | ||||
−0.546775 | + | 0.837280i | \(0.684145\pi\) | |||||||
\(150\) | 2.44949 | 0.200000 | ||||||||
\(151\) | 14.0000 | 1.13930 | 0.569652 | − | 0.821886i | \(-0.307078\pi\) | ||||
0.569652 | + | 0.821886i | \(0.307078\pi\) | |||||||
\(152\) | 2.20204 | 0.178609 | ||||||||
\(153\) | 0.550510 | 0.0445061 | ||||||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | 9.89898 | 0.795105 | ||||||||
\(156\) | −1.79796 | −0.143952 | ||||||||
\(157\) | 20.5959 | 1.64373 | 0.821867 | − | 0.569680i | \(-0.192933\pi\) | ||||
0.821867 | + | 0.569680i | \(0.192933\pi\) | |||||||
\(158\) | 9.79796 | 0.779484 | ||||||||
\(159\) | −5.44949 | −0.432173 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.44949 | 0.192450 | ||||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | 2.20204 | 0.171951 | ||||||||
\(165\) | 2.44949 | 0.190693 | ||||||||
\(166\) | 22.6515 | 1.75810 | ||||||||
\(167\) | −1.34847 | −0.104348 | −0.0521738 | − | 0.998638i | \(-0.516615\pi\) | ||||
−0.0521738 | + | 0.998638i | \(0.516615\pi\) | |||||||
\(168\) | 4.89898 | 0.377964 | ||||||||
\(169\) | −12.7980 | −0.984458 | ||||||||
\(170\) | 1.34847 | 0.103423 | ||||||||
\(171\) | 0.449490 | 0.0343733 | ||||||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | −19.5959 | −1.48985 | −0.744925 | − | 0.667148i | \(-0.767515\pi\) | ||||
−0.744925 | + | 0.667148i | \(0.767515\pi\) | |||||||
\(174\) | −10.6515 | −0.807490 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 9.79796 | 0.738549 | ||||||||
\(177\) | −4.34847 | −0.326851 | ||||||||
\(178\) | 17.3939 | 1.30373 | ||||||||
\(179\) | −6.00000 | −0.448461 | −0.224231 | − | 0.974536i | \(-0.571987\pi\) | ||||
−0.224231 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(180\) | 4.00000 | 0.298142 | ||||||||
\(181\) | −0.898979 | −0.0668206 | −0.0334103 | − | 0.999442i | \(-0.510637\pi\) | ||||
−0.0334103 | + | 0.999442i | \(0.510637\pi\) | |||||||
\(182\) | −1.10102 | −0.0816131 | ||||||||
\(183\) | −15.3485 | −1.13459 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.89898 | 0.433702 | ||||||||
\(186\) | 24.2474 | 1.77791 | ||||||||
\(187\) | 1.34847 | 0.0986098 | ||||||||
\(188\) | 14.2020 | 1.03579 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 1.10102 | 0.0798764 | ||||||||
\(191\) | −6.24745 | −0.452050 | −0.226025 | − | 0.974122i | \(-0.572573\pi\) | ||||
−0.226025 | + | 0.974122i | \(0.572573\pi\) | |||||||
\(192\) | −8.00000 | −0.577350 | ||||||||
\(193\) | 22.6969 | 1.63376 | 0.816881 | − | 0.576807i | \(-0.195701\pi\) | ||||
0.816881 | + | 0.576807i | \(0.195701\pi\) | |||||||
\(194\) | −31.5959 | −2.26845 | ||||||||
\(195\) | −0.449490 | −0.0321886 | ||||||||
\(196\) | −24.0000 | −1.71429 | ||||||||
\(197\) | −13.1010 | −0.933409 | −0.466705 | − | 0.884413i | \(-0.654559\pi\) | ||||
−0.466705 | + | 0.884413i | \(0.654559\pi\) | |||||||
\(198\) | 6.00000 | 0.426401 | ||||||||
\(199\) | −6.89898 | −0.489056 | −0.244528 | − | 0.969642i | \(-0.578633\pi\) | ||||
−0.244528 | + | 0.969642i | \(0.578633\pi\) | |||||||
\(200\) | 4.89898 | 0.346410 | ||||||||
\(201\) | 7.00000 | 0.493742 | ||||||||
\(202\) | −42.7423 | −3.00734 | ||||||||
\(203\) | −4.34847 | −0.305203 | ||||||||
\(204\) | 2.20204 | 0.154174 | ||||||||
\(205\) | 0.550510 | 0.0384493 | ||||||||
\(206\) | −40.8990 | −2.84957 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.79796 | −0.124666 | ||||||||
\(209\) | 1.10102 | 0.0761592 | ||||||||
\(210\) | 2.44949 | 0.169031 | ||||||||
\(211\) | 11.0000 | 0.757271 | 0.378636 | − | 0.925546i | \(-0.376393\pi\) | ||||
0.378636 | + | 0.925546i | \(0.376393\pi\) | |||||||
\(212\) | −21.7980 | −1.49709 | ||||||||
\(213\) | 10.3485 | 0.709065 | ||||||||
\(214\) | 1.34847 | 0.0921795 | ||||||||
\(215\) | −2.00000 | −0.136399 | ||||||||
\(216\) | 4.89898 | 0.333333 | ||||||||
\(217\) | 9.89898 | 0.671987 | ||||||||
\(218\) | −40.2929 | −2.72898 | ||||||||
\(219\) | 9.34847 | 0.631711 | ||||||||
\(220\) | 9.79796 | 0.660578 | ||||||||
\(221\) | −0.247449 | −0.0166452 | ||||||||
\(222\) | 14.4495 | 0.969786 | ||||||||
\(223\) | −17.5959 | −1.17831 | −0.589155 | − | 0.808020i | \(-0.700539\pi\) | ||||
−0.589155 | + | 0.808020i | \(0.700539\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 40.0454 | 2.66378 | ||||||||
\(227\) | −2.20204 | −0.146155 | −0.0730773 | − | 0.997326i | \(-0.523282\pi\) | ||||
−0.0730773 | + | 0.997326i | \(0.523282\pi\) | |||||||
\(228\) | 1.79796 | 0.119073 | ||||||||
\(229\) | −20.4949 | −1.35434 | −0.677170 | − | 0.735826i | \(-0.736794\pi\) | ||||
−0.677170 | + | 0.735826i | \(0.736794\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.44949 | 0.161165 | ||||||||
\(232\) | −21.3031 | −1.39861 | ||||||||
\(233\) | 2.20204 | 0.144261 | 0.0721303 | − | 0.997395i | \(-0.477020\pi\) | ||||
0.0721303 | + | 0.997395i | \(0.477020\pi\) | |||||||
\(234\) | −1.10102 | −0.0719760 | ||||||||
\(235\) | 3.55051 | 0.231610 | ||||||||
\(236\) | −17.3939 | −1.13224 | ||||||||
\(237\) | 4.00000 | 0.259828 | ||||||||
\(238\) | 1.34847 | 0.0874083 | ||||||||
\(239\) | 11.4495 | 0.740606 | 0.370303 | − | 0.928911i | \(-0.379254\pi\) | ||||
0.370303 | + | 0.928911i | \(0.379254\pi\) | |||||||
\(240\) | 4.00000 | 0.258199 | ||||||||
\(241\) | 14.6515 | 0.943788 | 0.471894 | − | 0.881655i | \(-0.343570\pi\) | ||||
0.471894 | + | 0.881655i | \(0.343570\pi\) | |||||||
\(242\) | −12.2474 | −0.787296 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −61.3939 | −3.93034 | ||||||||
\(245\) | −6.00000 | −0.383326 | ||||||||
\(246\) | 1.34847 | 0.0859753 | ||||||||
\(247\) | −0.202041 | −0.0128556 | ||||||||
\(248\) | 48.4949 | 3.07943 | ||||||||
\(249\) | 9.24745 | 0.586033 | ||||||||
\(250\) | 2.44949 | 0.154919 | ||||||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | 4.00000 | 0.251976 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −15.7980 | −0.991252 | ||||||||
\(255\) | 0.550510 | 0.0344743 | ||||||||
\(256\) | −32.0000 | −2.00000 | ||||||||
\(257\) | −10.6515 | −0.664424 | −0.332212 | − | 0.943205i | \(-0.607795\pi\) | ||||
−0.332212 | + | 0.943205i | \(0.607795\pi\) | |||||||
\(258\) | −4.89898 | −0.304997 | ||||||||
\(259\) | 5.89898 | 0.366545 | ||||||||
\(260\) | −1.79796 | −0.111505 | ||||||||
\(261\) | −4.34847 | −0.269163 | ||||||||
\(262\) | 48.0000 | 2.96545 | ||||||||
\(263\) | −2.75255 | −0.169730 | −0.0848648 | − | 0.996392i | \(-0.527046\pi\) | ||||
−0.0848648 | + | 0.996392i | \(0.527046\pi\) | |||||||
\(264\) | 12.0000 | 0.738549 | ||||||||
\(265\) | −5.44949 | −0.334759 | ||||||||
\(266\) | 1.10102 | 0.0675079 | ||||||||
\(267\) | 7.10102 | 0.434575 | ||||||||
\(268\) | 28.0000 | 1.71037 | ||||||||
\(269\) | −0.550510 | −0.0335652 | −0.0167826 | − | 0.999859i | \(-0.505342\pi\) | ||||
−0.0167826 | + | 0.999859i | \(0.505342\pi\) | |||||||
\(270\) | 2.44949 | 0.149071 | ||||||||
\(271\) | 2.30306 | 0.139901 | 0.0699505 | − | 0.997550i | \(-0.477716\pi\) | ||||
0.0699505 | + | 0.997550i | \(0.477716\pi\) | |||||||
\(272\) | 2.20204 | 0.133518 | ||||||||
\(273\) | −0.449490 | −0.0272044 | ||||||||
\(274\) | 17.3939 | 1.05080 | ||||||||
\(275\) | 2.44949 | 0.147710 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | 36.2474 | 2.17398 | ||||||||
\(279\) | 9.89898 | 0.592636 | ||||||||
\(280\) | 4.89898 | 0.292770 | ||||||||
\(281\) | 4.65153 | 0.277487 | 0.138744 | − | 0.990328i | \(-0.455694\pi\) | ||||
0.138744 | + | 0.990328i | \(0.455694\pi\) | |||||||
\(282\) | 8.69694 | 0.517895 | ||||||||
\(283\) | 11.8990 | 0.707321 | 0.353660 | − | 0.935374i | \(-0.384937\pi\) | ||||
0.353660 | + | 0.935374i | \(0.384937\pi\) | |||||||
\(284\) | 41.3939 | 2.45627 | ||||||||
\(285\) | 0.449490 | 0.0266255 | ||||||||
\(286\) | −2.69694 | −0.159473 | ||||||||
\(287\) | 0.550510 | 0.0324956 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6969 | −0.982173 | ||||||||
\(290\) | −10.6515 | −0.625479 | ||||||||
\(291\) | −12.8990 | −0.756152 | ||||||||
\(292\) | 37.3939 | 2.18831 | ||||||||
\(293\) | −3.24745 | −0.189718 | −0.0948590 | − | 0.995491i | \(-0.530240\pi\) | ||||
−0.0948590 | + | 0.995491i | \(0.530240\pi\) | |||||||
\(294\) | −14.6969 | −0.857143 | ||||||||
\(295\) | −4.34847 | −0.253178 | ||||||||
\(296\) | 28.8990 | 1.67972 | ||||||||
\(297\) | 2.44949 | 0.142134 | ||||||||
\(298\) | −32.6969 | −1.89408 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | −2.00000 | −0.115278 | ||||||||
\(302\) | 34.2929 | 1.97333 | ||||||||
\(303\) | −17.4495 | −1.00245 | ||||||||
\(304\) | 1.79796 | 0.103120 | ||||||||
\(305\) | −15.3485 | −0.878851 | ||||||||
\(306\) | 1.34847 | 0.0770869 | ||||||||
\(307\) | −17.3485 | −0.990129 | −0.495065 | − | 0.868856i | \(-0.664856\pi\) | ||||
−0.495065 | + | 0.868856i | \(0.664856\pi\) | |||||||
\(308\) | 9.79796 | 0.558291 | ||||||||
\(309\) | −16.6969 | −0.949856 | ||||||||
\(310\) | 24.2474 | 1.37716 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | −2.20204 | −0.124666 | ||||||||
\(313\) | 9.69694 | 0.548103 | 0.274052 | − | 0.961715i | \(-0.411636\pi\) | ||||
0.274052 | + | 0.961715i | \(0.411636\pi\) | |||||||
\(314\) | 50.4495 | 2.84703 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 16.0000 | 0.900070 | ||||||||
\(317\) | −18.2474 | −1.02488 | −0.512439 | − | 0.858723i | \(-0.671258\pi\) | ||||
−0.512439 | + | 0.858723i | \(0.671258\pi\) | |||||||
\(318\) | −13.3485 | −0.748545 | ||||||||
\(319\) | −10.6515 | −0.596371 | ||||||||
\(320\) | −8.00000 | −0.447214 | ||||||||
\(321\) | 0.550510 | 0.0307265 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.247449 | 0.0137684 | ||||||||
\(324\) | 4.00000 | 0.222222 | ||||||||
\(325\) | −0.449490 | −0.0249332 | ||||||||
\(326\) | −24.4949 | −1.35665 | ||||||||
\(327\) | −16.4495 | −0.909659 | ||||||||
\(328\) | 2.69694 | 0.148914 | ||||||||
\(329\) | 3.55051 | 0.195746 | ||||||||
\(330\) | 6.00000 | 0.330289 | ||||||||
\(331\) | −14.5959 | −0.802264 | −0.401132 | − | 0.916020i | \(-0.631383\pi\) | ||||
−0.401132 | + | 0.916020i | \(0.631383\pi\) | |||||||
\(332\) | 36.9898 | 2.03008 | ||||||||
\(333\) | 5.89898 | 0.323262 | ||||||||
\(334\) | −3.30306 | −0.180735 | ||||||||
\(335\) | 7.00000 | 0.382451 | ||||||||
\(336\) | 4.00000 | 0.218218 | ||||||||
\(337\) | 0.202041 | 0.0110059 | 0.00550294 | − | 0.999985i | \(-0.498248\pi\) | ||||
0.00550294 | + | 0.999985i | \(0.498248\pi\) | |||||||
\(338\) | −31.3485 | −1.70513 | ||||||||
\(339\) | 16.3485 | 0.887927 | ||||||||
\(340\) | 2.20204 | 0.119422 | ||||||||
\(341\) | 24.2474 | 1.31307 | ||||||||
\(342\) | 1.10102 | 0.0595364 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −9.79796 | −0.528271 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −48.0000 | −2.58050 | ||||||||
\(347\) | −19.1010 | −1.02540 | −0.512698 | − | 0.858569i | \(-0.671354\pi\) | ||||
−0.512698 | + | 0.858569i | \(0.671354\pi\) | |||||||
\(348\) | −17.3939 | −0.932410 | ||||||||
\(349\) | −25.4949 | −1.36471 | −0.682355 | − | 0.731021i | \(-0.739044\pi\) | ||||
−0.682355 | + | 0.731021i | \(0.739044\pi\) | |||||||
\(350\) | 2.44949 | 0.130931 | ||||||||
\(351\) | −0.449490 | −0.0239920 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.4495 | −1.08842 | −0.544208 | − | 0.838950i | \(-0.683170\pi\) | ||||
−0.544208 | + | 0.838950i | \(0.683170\pi\) | |||||||
\(354\) | −10.6515 | −0.566122 | ||||||||
\(355\) | 10.3485 | 0.549240 | ||||||||
\(356\) | 28.4041 | 1.50541 | ||||||||
\(357\) | 0.550510 | 0.0291361 | ||||||||
\(358\) | −14.6969 | −0.776757 | ||||||||
\(359\) | 8.44949 | 0.445947 | 0.222974 | − | 0.974825i | \(-0.428424\pi\) | ||||
0.222974 | + | 0.974825i | \(0.428424\pi\) | |||||||
\(360\) | 4.89898 | 0.258199 | ||||||||
\(361\) | −18.7980 | −0.989366 | ||||||||
\(362\) | −2.20204 | −0.115737 | ||||||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | −1.79796 | −0.0942387 | ||||||||
\(365\) | 9.34847 | 0.489321 | ||||||||
\(366\) | −37.5959 | −1.96517 | ||||||||
\(367\) | 15.6969 | 0.819374 | 0.409687 | − | 0.912226i | \(-0.365638\pi\) | ||||
0.409687 | + | 0.912226i | \(0.365638\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.550510 | 0.0286584 | ||||||||
\(370\) | 14.4495 | 0.751193 | ||||||||
\(371\) | −5.44949 | −0.282923 | ||||||||
\(372\) | 39.5959 | 2.05295 | ||||||||
\(373\) | 11.5959 | 0.600414 | 0.300207 | − | 0.953874i | \(-0.402944\pi\) | ||||
0.300207 | + | 0.953874i | \(0.402944\pi\) | |||||||
\(374\) | 3.30306 | 0.170797 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 17.3939 | 0.897021 | ||||||||
\(377\) | 1.95459 | 0.100667 | ||||||||
\(378\) | 2.44949 | 0.125988 | ||||||||
\(379\) | 33.3939 | 1.71533 | 0.857664 | − | 0.514210i | \(-0.171915\pi\) | ||||
0.857664 | + | 0.514210i | \(0.171915\pi\) | |||||||
\(380\) | 1.79796 | 0.0922333 | ||||||||
\(381\) | −6.44949 | −0.330417 | ||||||||
\(382\) | −15.3031 | −0.782973 | ||||||||
\(383\) | −16.3485 | −0.835368 | −0.417684 | − | 0.908592i | \(-0.637158\pi\) | ||||
−0.417684 | + | 0.908592i | \(0.637158\pi\) | |||||||
\(384\) | −19.5959 | −1.00000 | ||||||||
\(385\) | 2.44949 | 0.124838 | ||||||||
\(386\) | 55.5959 | 2.82976 | ||||||||
\(387\) | −2.00000 | −0.101666 | ||||||||
\(388\) | −51.5959 | −2.61939 | ||||||||
\(389\) | 32.6969 | 1.65780 | 0.828900 | − | 0.559396i | \(-0.188967\pi\) | ||||
0.828900 | + | 0.559396i | \(0.188967\pi\) | |||||||
\(390\) | −1.10102 | −0.0557523 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −29.3939 | −1.48461 | ||||||||
\(393\) | 19.5959 | 0.988483 | ||||||||
\(394\) | −32.0908 | −1.61671 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 9.79796 | 0.492366 | ||||||||
\(397\) | 5.79796 | 0.290991 | 0.145496 | − | 0.989359i | \(-0.453522\pi\) | ||||
0.145496 | + | 0.989359i | \(0.453522\pi\) | |||||||
\(398\) | −16.8990 | −0.847069 | ||||||||
\(399\) | 0.449490 | 0.0225026 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | 22.8990 | 1.14352 | 0.571760 | − | 0.820421i | \(-0.306261\pi\) | ||||
0.571760 | + | 0.820421i | \(0.306261\pi\) | |||||||
\(402\) | 17.1464 | 0.855186 | ||||||||
\(403\) | −4.44949 | −0.221645 | ||||||||
\(404\) | −69.7980 | −3.47258 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −10.6515 | −0.528627 | ||||||||
\(407\) | 14.4495 | 0.716235 | ||||||||
\(408\) | 2.69694 | 0.133518 | ||||||||
\(409\) | 12.1010 | 0.598357 | 0.299178 | − | 0.954197i | \(-0.403287\pi\) | ||||
0.299178 | + | 0.954197i | \(0.403287\pi\) | |||||||
\(410\) | 1.34847 | 0.0665961 | ||||||||
\(411\) | 7.10102 | 0.350268 | ||||||||
\(412\) | −66.7878 | −3.29040 | ||||||||
\(413\) | −4.34847 | −0.213974 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.24745 | 0.453939 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.7980 | 0.724659 | ||||||||
\(418\) | 2.69694 | 0.131912 | ||||||||
\(419\) | −38.4495 | −1.87838 | −0.939190 | − | 0.343397i | \(-0.888422\pi\) | ||||
−0.939190 | + | 0.343397i | \(0.888422\pi\) | |||||||
\(420\) | 4.00000 | 0.195180 | ||||||||
\(421\) | −2.24745 | −0.109534 | −0.0547670 | − | 0.998499i | \(-0.517442\pi\) | ||||
−0.0547670 | + | 0.998499i | \(0.517442\pi\) | |||||||
\(422\) | 26.9444 | 1.31163 | ||||||||
\(423\) | 3.55051 | 0.172632 | ||||||||
\(424\) | −26.6969 | −1.29652 | ||||||||
\(425\) | 0.550510 | 0.0267037 | ||||||||
\(426\) | 25.3485 | 1.22814 | ||||||||
\(427\) | −15.3485 | −0.742764 | ||||||||
\(428\) | 2.20204 | 0.106440 | ||||||||
\(429\) | −1.10102 | −0.0531578 | ||||||||
\(430\) | −4.89898 | −0.236250 | ||||||||
\(431\) | −24.4949 | −1.17988 | −0.589939 | − | 0.807448i | \(-0.700848\pi\) | ||||
−0.589939 | + | 0.807448i | \(0.700848\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | 16.7980 | 0.807258 | 0.403629 | − | 0.914923i | \(-0.367749\pi\) | ||||
0.403629 | + | 0.914923i | \(0.367749\pi\) | |||||||
\(434\) | 24.2474 | 1.16391 | ||||||||
\(435\) | −4.34847 | −0.208493 | ||||||||
\(436\) | −65.7980 | −3.15115 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 22.8990 | 1.09416 | ||||||||
\(439\) | −7.30306 | −0.348556 | −0.174278 | − | 0.984696i | \(-0.555759\pi\) | ||||
−0.174278 | + | 0.984696i | \(0.555759\pi\) | |||||||
\(440\) | 12.0000 | 0.572078 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | −0.606123 | −0.0288303 | ||||||||
\(443\) | −15.5505 | −0.738827 | −0.369414 | − | 0.929265i | \(-0.620441\pi\) | ||||
−0.369414 | + | 0.929265i | \(0.620441\pi\) | |||||||
\(444\) | 23.5959 | 1.11981 | ||||||||
\(445\) | 7.10102 | 0.336621 | ||||||||
\(446\) | −43.1010 | −2.04089 | ||||||||
\(447\) | −13.3485 | −0.631361 | ||||||||
\(448\) | −8.00000 | −0.377964 | ||||||||
\(449\) | 3.24745 | 0.153257 | 0.0766283 | − | 0.997060i | \(-0.475585\pi\) | ||||
0.0766283 | + | 0.997060i | \(0.475585\pi\) | |||||||
\(450\) | 2.44949 | 0.115470 | ||||||||
\(451\) | 1.34847 | 0.0634969 | ||||||||
\(452\) | 65.3939 | 3.07587 | ||||||||
\(453\) | 14.0000 | 0.657777 | ||||||||
\(454\) | −5.39388 | −0.253147 | ||||||||
\(455\) | −0.449490 | −0.0210724 | ||||||||
\(456\) | 2.20204 | 0.103120 | ||||||||
\(457\) | −9.89898 | −0.463055 | −0.231527 | − | 0.972828i | \(-0.574372\pi\) | ||||
−0.231527 | + | 0.972828i | \(0.574372\pi\) | |||||||
\(458\) | −50.2020 | −2.34579 | ||||||||
\(459\) | 0.550510 | 0.0256956 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.4949 | 1.42029 | 0.710144 | − | 0.704056i | \(-0.248630\pi\) | ||||
0.710144 | + | 0.704056i | \(0.248630\pi\) | |||||||
\(462\) | 6.00000 | 0.279145 | ||||||||
\(463\) | 28.9444 | 1.34516 | 0.672580 | − | 0.740025i | \(-0.265186\pi\) | ||||
0.672580 | + | 0.740025i | \(0.265186\pi\) | |||||||
\(464\) | −17.3939 | −0.807490 | ||||||||
\(465\) | 9.89898 | 0.459054 | ||||||||
\(466\) | 5.39388 | 0.249867 | ||||||||
\(467\) | −28.8434 | −1.33471 | −0.667356 | − | 0.744739i | \(-0.732574\pi\) | ||||
−0.667356 | + | 0.744739i | \(0.732574\pi\) | |||||||
\(468\) | −1.79796 | −0.0831107 | ||||||||
\(469\) | 7.00000 | 0.323230 | ||||||||
\(470\) | 8.69694 | 0.401160 | ||||||||
\(471\) | 20.5959 | 0.949010 | ||||||||
\(472\) | −21.3031 | −0.980553 | ||||||||
\(473\) | −4.89898 | −0.225255 | ||||||||
\(474\) | 9.79796 | 0.450035 | ||||||||
\(475\) | 0.449490 | 0.0206240 | ||||||||
\(476\) | 2.20204 | 0.100930 | ||||||||
\(477\) | −5.44949 | −0.249515 | ||||||||
\(478\) | 28.0454 | 1.28277 | ||||||||
\(479\) | 20.9444 | 0.956973 | 0.478487 | − | 0.878095i | \(-0.341185\pi\) | ||||
0.478487 | + | 0.878095i | \(0.341185\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.65153 | −0.120899 | ||||||||
\(482\) | 35.8888 | 1.63469 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20.0000 | −0.909091 | ||||||||
\(485\) | −12.8990 | −0.585712 | ||||||||
\(486\) | 2.44949 | 0.111111 | ||||||||
\(487\) | 34.9444 | 1.58348 | 0.791741 | − | 0.610857i | \(-0.209175\pi\) | ||||
0.791741 | + | 0.610857i | \(0.209175\pi\) | |||||||
\(488\) | −75.1918 | −3.40377 | ||||||||
\(489\) | −10.0000 | −0.452216 | ||||||||
\(490\) | −14.6969 | −0.663940 | ||||||||
\(491\) | 17.4495 | 0.787484 | 0.393742 | − | 0.919221i | \(-0.371180\pi\) | ||||
0.393742 | + | 0.919221i | \(0.371180\pi\) | |||||||
\(492\) | 2.20204 | 0.0992757 | ||||||||
\(493\) | −2.39388 | −0.107815 | ||||||||
\(494\) | −0.494897 | −0.0222665 | ||||||||
\(495\) | 2.44949 | 0.110096 | ||||||||
\(496\) | 39.5959 | 1.77791 | ||||||||
\(497\) | 10.3485 | 0.464192 | ||||||||
\(498\) | 22.6515 | 1.01504 | ||||||||
\(499\) | −1.00000 | −0.0447661 | −0.0223831 | − | 0.999749i | \(-0.507125\pi\) | ||||
−0.0223831 | + | 0.999749i | \(0.507125\pi\) | |||||||
\(500\) | 4.00000 | 0.178885 | ||||||||
\(501\) | −1.34847 | −0.0602452 | ||||||||
\(502\) | −44.0908 | −1.96787 | ||||||||
\(503\) | 37.0454 | 1.65177 | 0.825887 | − | 0.563836i | \(-0.190675\pi\) | ||||
0.825887 | + | 0.563836i | \(0.190675\pi\) | |||||||
\(504\) | 4.89898 | 0.218218 | ||||||||
\(505\) | −17.4495 | −0.776492 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.7980 | −0.568377 | ||||||||
\(508\) | −25.7980 | −1.14460 | ||||||||
\(509\) | 19.1010 | 0.846638 | 0.423319 | − | 0.905981i | \(-0.360865\pi\) | ||||
0.423319 | + | 0.905981i | \(0.360865\pi\) | |||||||
\(510\) | 1.34847 | 0.0597112 | ||||||||
\(511\) | 9.34847 | 0.413552 | ||||||||
\(512\) | −39.1918 | −1.73205 | ||||||||
\(513\) | 0.449490 | 0.0198455 | ||||||||
\(514\) | −26.0908 | −1.15082 | ||||||||
\(515\) | −16.6969 | −0.735755 | ||||||||
\(516\) | −8.00000 | −0.352180 | ||||||||
\(517\) | 8.69694 | 0.382491 | ||||||||
\(518\) | 14.4495 | 0.634874 | ||||||||
\(519\) | −19.5959 | −0.860165 | ||||||||
\(520\) | −2.20204 | −0.0965659 | ||||||||
\(521\) | −19.8434 | −0.869354 | −0.434677 | − | 0.900587i | \(-0.643137\pi\) | ||||
−0.434677 | + | 0.900587i | \(0.643137\pi\) | |||||||
\(522\) | −10.6515 | −0.466205 | ||||||||
\(523\) | −25.3939 | −1.11040 | −0.555198 | − | 0.831718i | \(-0.687358\pi\) | ||||
−0.555198 | + | 0.831718i | \(0.687358\pi\) | |||||||
\(524\) | 78.3837 | 3.42421 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | −6.74235 | −0.293980 | ||||||||
\(527\) | 5.44949 | 0.237384 | ||||||||
\(528\) | 9.79796 | 0.426401 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −13.3485 | −0.579820 | ||||||||
\(531\) | −4.34847 | −0.188707 | ||||||||
\(532\) | 1.79796 | 0.0779514 | ||||||||
\(533\) | −0.247449 | −0.0107182 | ||||||||
\(534\) | 17.3939 | 0.752707 | ||||||||
\(535\) | 0.550510 | 0.0238006 | ||||||||
\(536\) | 34.2929 | 1.48123 | ||||||||
\(537\) | −6.00000 | −0.258919 | ||||||||
\(538\) | −1.34847 | −0.0581366 | ||||||||
\(539\) | −14.6969 | −0.633042 | ||||||||
\(540\) | 4.00000 | 0.172133 | ||||||||
\(541\) | 3.10102 | 0.133323 | 0.0666616 | − | 0.997776i | \(-0.478765\pi\) | ||||
0.0666616 | + | 0.997776i | \(0.478765\pi\) | |||||||
\(542\) | 5.64133 | 0.242316 | ||||||||
\(543\) | −0.898979 | −0.0385789 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.4495 | −0.704619 | ||||||||
\(546\) | −1.10102 | −0.0471193 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 28.4041 | 1.21336 | ||||||||
\(549\) | −15.3485 | −0.655057 | ||||||||
\(550\) | 6.00000 | 0.255841 | ||||||||
\(551\) | −1.95459 | −0.0832684 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | 0.170097 | ||||||||
\(554\) | −24.4949 | −1.04069 | ||||||||
\(555\) | 5.89898 | 0.250398 | ||||||||
\(556\) | 59.1918 | 2.51029 | ||||||||
\(557\) | −25.0454 | −1.06121 | −0.530604 | − | 0.847620i | \(-0.678035\pi\) | ||||
−0.530604 | + | 0.847620i | \(0.678035\pi\) | |||||||
\(558\) | 24.2474 | 1.02648 | ||||||||
\(559\) | 0.898979 | 0.0380228 | ||||||||
\(560\) | 4.00000 | 0.169031 | ||||||||
\(561\) | 1.34847 | 0.0569324 | ||||||||
\(562\) | 11.3939 | 0.480622 | ||||||||
\(563\) | −0.550510 | −0.0232012 | −0.0116006 | − | 0.999933i | \(-0.503693\pi\) | ||||
−0.0116006 | + | 0.999933i | \(0.503693\pi\) | |||||||
\(564\) | 14.2020 | 0.598014 | ||||||||
\(565\) | 16.3485 | 0.687785 | ||||||||
\(566\) | 29.1464 | 1.22512 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 50.6969 | 2.12720 | ||||||||
\(569\) | −40.2929 | −1.68916 | −0.844582 | − | 0.535426i | \(-0.820151\pi\) | ||||
−0.844582 | + | 0.535426i | \(0.820151\pi\) | |||||||
\(570\) | 1.10102 | 0.0461167 | ||||||||
\(571\) | 21.1464 | 0.884950 | 0.442475 | − | 0.896781i | \(-0.354100\pi\) | ||||
0.442475 | + | 0.896781i | \(0.354100\pi\) | |||||||
\(572\) | −4.40408 | −0.184144 | ||||||||
\(573\) | −6.24745 | −0.260991 | ||||||||
\(574\) | 1.34847 | 0.0562840 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | −28.0000 | −1.16566 | −0.582828 | − | 0.812596i | \(-0.698054\pi\) | ||||
−0.582828 | + | 0.812596i | \(0.698054\pi\) | |||||||
\(578\) | −40.8990 | −1.70117 | ||||||||
\(579\) | 22.6969 | 0.943253 | ||||||||
\(580\) | −17.3939 | −0.722241 | ||||||||
\(581\) | 9.24745 | 0.383649 | ||||||||
\(582\) | −31.5959 | −1.30969 | ||||||||
\(583\) | −13.3485 | −0.552837 | ||||||||
\(584\) | 45.7980 | 1.89513 | ||||||||
\(585\) | −0.449490 | −0.0185841 | ||||||||
\(586\) | −7.95459 | −0.328601 | ||||||||
\(587\) | −6.00000 | −0.247647 | −0.123823 | − | 0.992304i | \(-0.539516\pi\) | ||||
−0.123823 | + | 0.992304i | \(0.539516\pi\) | |||||||
\(588\) | −24.0000 | −0.989743 | ||||||||
\(589\) | 4.44949 | 0.183338 | ||||||||
\(590\) | −10.6515 | −0.438517 | ||||||||
\(591\) | −13.1010 | −0.538904 | ||||||||
\(592\) | 23.5959 | 0.969786 | ||||||||
\(593\) | 32.4495 | 1.33254 | 0.666270 | − | 0.745710i | \(-0.267890\pi\) | ||||
0.666270 | + | 0.745710i | \(0.267890\pi\) | |||||||
\(594\) | 6.00000 | 0.246183 | ||||||||
\(595\) | 0.550510 | 0.0225687 | ||||||||
\(596\) | −53.3939 | −2.18710 | ||||||||
\(597\) | −6.89898 | −0.282356 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.6969 | 1.09081 | 0.545404 | − | 0.838174i | \(-0.316376\pi\) | ||||
0.545404 | + | 0.838174i | \(0.316376\pi\) | |||||||
\(600\) | 4.89898 | 0.200000 | ||||||||
\(601\) | 5.00000 | 0.203954 | 0.101977 | − | 0.994787i | \(-0.467483\pi\) | ||||
0.101977 | + | 0.994787i | \(0.467483\pi\) | |||||||
\(602\) | −4.89898 | −0.199667 | ||||||||
\(603\) | 7.00000 | 0.285062 | ||||||||
\(604\) | 56.0000 | 2.27861 | ||||||||
\(605\) | −5.00000 | −0.203279 | ||||||||
\(606\) | −42.7423 | −1.73629 | ||||||||
\(607\) | 8.24745 | 0.334754 | 0.167377 | − | 0.985893i | \(-0.446470\pi\) | ||||
0.167377 | + | 0.985893i | \(0.446470\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.34847 | −0.176209 | ||||||||
\(610\) | −37.5959 | −1.52221 | ||||||||
\(611\) | −1.59592 | −0.0645639 | ||||||||
\(612\) | 2.20204 | 0.0890122 | ||||||||
\(613\) | −14.0000 | −0.565455 | −0.282727 | − | 0.959200i | \(-0.591239\pi\) | ||||
−0.282727 | + | 0.959200i | \(0.591239\pi\) | |||||||
\(614\) | −42.4949 | −1.71495 | ||||||||
\(615\) | 0.550510 | 0.0221987 | ||||||||
\(616\) | 12.0000 | 0.483494 | ||||||||
\(617\) | −17.4495 | −0.702490 | −0.351245 | − | 0.936284i | \(-0.614242\pi\) | ||||
−0.351245 | + | 0.936284i | \(0.614242\pi\) | |||||||
\(618\) | −40.8990 | −1.64520 | ||||||||
\(619\) | 4.00000 | 0.160774 | 0.0803868 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803868 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(620\) | 39.5959 | 1.59021 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 29.3939 | 1.17859 | ||||||||
\(623\) | 7.10102 | 0.284496 | ||||||||
\(624\) | −1.79796 | −0.0719760 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.7526 | 0.949343 | ||||||||
\(627\) | 1.10102 | 0.0439705 | ||||||||
\(628\) | 82.3837 | 3.28747 | ||||||||
\(629\) | 3.24745 | 0.129484 | ||||||||
\(630\) | 2.44949 | 0.0975900 | ||||||||
\(631\) | −34.4495 | −1.37141 | −0.685706 | − | 0.727878i | \(-0.740507\pi\) | ||||
−0.685706 | + | 0.727878i | \(0.740507\pi\) | |||||||
\(632\) | 19.5959 | 0.779484 | ||||||||
\(633\) | 11.0000 | 0.437211 | ||||||||
\(634\) | −44.6969 | −1.77514 | ||||||||
\(635\) | −6.44949 | −0.255940 | ||||||||
\(636\) | −21.7980 | −0.864345 | ||||||||
\(637\) | 2.69694 | 0.106857 | ||||||||
\(638\) | −26.0908 | −1.03295 | ||||||||
\(639\) | 10.3485 | 0.409379 | ||||||||
\(640\) | −19.5959 | −0.774597 | ||||||||
\(641\) | 26.9444 | 1.06424 | 0.532120 | − | 0.846669i | \(-0.321396\pi\) | ||||
0.532120 | + | 0.846669i | \(0.321396\pi\) | |||||||
\(642\) | 1.34847 | 0.0532198 | ||||||||
\(643\) | −19.6969 | −0.776771 | −0.388386 | − | 0.921497i | \(-0.626967\pi\) | ||||
−0.388386 | + | 0.921497i | \(0.626967\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.00000 | −0.0787499 | ||||||||
\(646\) | 0.606123 | 0.0238476 | ||||||||
\(647\) | 46.0454 | 1.81023 | 0.905116 | − | 0.425165i | \(-0.139784\pi\) | ||||
0.905116 | + | 0.425165i | \(0.139784\pi\) | |||||||
\(648\) | 4.89898 | 0.192450 | ||||||||
\(649\) | −10.6515 | −0.418109 | ||||||||
\(650\) | −1.10102 | −0.0431856 | ||||||||
\(651\) | 9.89898 | 0.387972 | ||||||||
\(652\) | −40.0000 | −1.56652 | ||||||||
\(653\) | −19.8434 | −0.776531 | −0.388265 | − | 0.921548i | \(-0.626926\pi\) | ||||
−0.388265 | + | 0.921548i | \(0.626926\pi\) | |||||||
\(654\) | −40.2929 | −1.57558 | ||||||||
\(655\) | 19.5959 | 0.765676 | ||||||||
\(656\) | 2.20204 | 0.0859753 | ||||||||
\(657\) | 9.34847 | 0.364719 | ||||||||
\(658\) | 8.69694 | 0.339042 | ||||||||
\(659\) | −29.1464 | −1.13538 | −0.567692 | − | 0.823241i | \(-0.692163\pi\) | ||||
−0.567692 | + | 0.823241i | \(0.692163\pi\) | |||||||
\(660\) | 9.79796 | 0.381385 | ||||||||
\(661\) | 42.0908 | 1.63714 | 0.818571 | − | 0.574405i | \(-0.194766\pi\) | ||||
0.818571 | + | 0.574405i | \(0.194766\pi\) | |||||||
\(662\) | −35.7526 | −1.38956 | ||||||||
\(663\) | −0.247449 | −0.00961011 | ||||||||
\(664\) | 45.3031 | 1.75810 | ||||||||
\(665\) | 0.449490 | 0.0174305 | ||||||||
\(666\) | 14.4495 | 0.559906 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −5.39388 | −0.208695 | ||||||||
\(669\) | −17.5959 | −0.680297 | ||||||||
\(670\) | 17.1464 | 0.662424 | ||||||||
\(671\) | −37.5959 | −1.45137 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.5505 | 0.676522 | 0.338261 | − | 0.941052i | \(-0.390161\pi\) | ||||
0.338261 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(674\) | 0.494897 | 0.0190627 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −51.1918 | −1.96892 | ||||||||
\(677\) | 17.4495 | 0.670638 | 0.335319 | − | 0.942105i | \(-0.391156\pi\) | ||||
0.335319 | + | 0.942105i | \(0.391156\pi\) | |||||||
\(678\) | 40.0454 | 1.53793 | ||||||||
\(679\) | −12.8990 | −0.495017 | ||||||||
\(680\) | 2.69694 | 0.103423 | ||||||||
\(681\) | −2.20204 | −0.0843824 | ||||||||
\(682\) | 59.3939 | 2.27431 | ||||||||
\(683\) | −6.24745 | −0.239052 | −0.119526 | − | 0.992831i | \(-0.538137\pi\) | ||||
−0.119526 | + | 0.992831i | \(0.538137\pi\) | |||||||
\(684\) | 1.79796 | 0.0687467 | ||||||||
\(685\) | 7.10102 | 0.271316 | ||||||||
\(686\) | −31.8434 | −1.21579 | ||||||||
\(687\) | −20.4949 | −0.781929 | ||||||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | 2.44949 | 0.0933181 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.7980 | 1.36182 | 0.680909 | − | 0.732368i | \(-0.261585\pi\) | ||||
0.680909 | + | 0.732368i | \(0.261585\pi\) | |||||||
\(692\) | −78.3837 | −2.97970 | ||||||||
\(693\) | 2.44949 | 0.0930484 | ||||||||
\(694\) | −46.7878 | −1.77604 | ||||||||
\(695\) | 14.7980 | 0.561319 | ||||||||
\(696\) | −21.3031 | −0.807490 | ||||||||
\(697\) | 0.303062 | 0.0114793 | ||||||||
\(698\) | −62.4495 | −2.36375 | ||||||||
\(699\) | 2.20204 | 0.0832888 | ||||||||
\(700\) | 4.00000 | 0.151186 | ||||||||
\(701\) | 7.95459 | 0.300441 | 0.150220 | − | 0.988653i | \(-0.452002\pi\) | ||||
0.150220 | + | 0.988653i | \(0.452002\pi\) | |||||||
\(702\) | −1.10102 | −0.0415553 | ||||||||
\(703\) | 2.65153 | 0.100004 | ||||||||
\(704\) | −19.5959 | −0.738549 | ||||||||
\(705\) | 3.55051 | 0.133720 | ||||||||
\(706\) | −50.0908 | −1.88519 | ||||||||
\(707\) | −17.4495 | −0.656256 | ||||||||
\(708\) | −17.3939 | −0.653702 | ||||||||
\(709\) | −44.7423 | −1.68033 | −0.840167 | − | 0.542328i | \(-0.817543\pi\) | ||||
−0.840167 | + | 0.542328i | \(0.817543\pi\) | |||||||
\(710\) | 25.3485 | 0.951311 | ||||||||
\(711\) | 4.00000 | 0.150012 | ||||||||
\(712\) | 34.7878 | 1.30373 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 1.34847 | 0.0504652 | ||||||||
\(715\) | −1.10102 | −0.0411758 | ||||||||
\(716\) | −24.0000 | −0.896922 | ||||||||
\(717\) | 11.4495 | 0.427589 | ||||||||
\(718\) | 20.6969 | 0.772403 | ||||||||
\(719\) | 41.9444 | 1.56426 | 0.782131 | − | 0.623114i | \(-0.214133\pi\) | ||||
0.782131 | + | 0.623114i | \(0.214133\pi\) | |||||||
\(720\) | 4.00000 | 0.149071 | ||||||||
\(721\) | −16.6969 | −0.621826 | ||||||||
\(722\) | −46.0454 | −1.71363 | ||||||||
\(723\) | 14.6515 | 0.544896 | ||||||||
\(724\) | −3.59592 | −0.133641 | ||||||||
\(725\) | −4.34847 | −0.161498 | ||||||||
\(726\) | −12.2474 | −0.454545 | ||||||||
\(727\) | 45.6969 | 1.69481 | 0.847403 | − | 0.530951i | \(-0.178165\pi\) | ||||
0.847403 | + | 0.530951i | \(0.178165\pi\) | |||||||
\(728\) | −2.20204 | −0.0816131 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 22.8990 | 0.847529 | ||||||||
\(731\) | −1.10102 | −0.0407227 | ||||||||
\(732\) | −61.3939 | −2.26918 | ||||||||
\(733\) | −30.5959 | −1.13009 | −0.565043 | − | 0.825061i | \(-0.691140\pi\) | ||||
−0.565043 | + | 0.825061i | \(0.691140\pi\) | |||||||
\(734\) | 38.4495 | 1.41920 | ||||||||
\(735\) | −6.00000 | −0.221313 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.1464 | 0.631597 | ||||||||
\(738\) | 1.34847 | 0.0496378 | ||||||||
\(739\) | −28.7980 | −1.05935 | −0.529675 | − | 0.848201i | \(-0.677686\pi\) | ||||
−0.529675 | + | 0.848201i | \(0.677686\pi\) | |||||||
\(740\) | 23.5959 | 0.867403 | ||||||||
\(741\) | −0.202041 | −0.00742216 | ||||||||
\(742\) | −13.3485 | −0.490038 | ||||||||
\(743\) | 2.20204 | 0.0807851 | 0.0403925 | − | 0.999184i | \(-0.487139\pi\) | ||||
0.0403925 | + | 0.999184i | \(0.487139\pi\) | |||||||
\(744\) | 48.4949 | 1.77791 | ||||||||
\(745\) | −13.3485 | −0.489050 | ||||||||
\(746\) | 28.4041 | 1.03995 | ||||||||
\(747\) | 9.24745 | 0.338346 | ||||||||
\(748\) | 5.39388 | 0.197220 | ||||||||
\(749\) | 0.550510 | 0.0201152 | ||||||||
\(750\) | 2.44949 | 0.0894427 | ||||||||
\(751\) | −45.3485 | −1.65479 | −0.827395 | − | 0.561621i | \(-0.810178\pi\) | ||||
−0.827395 | + | 0.561621i | \(0.810178\pi\) | |||||||
\(752\) | 14.2020 | 0.517895 | ||||||||
\(753\) | −18.0000 | −0.655956 | ||||||||
\(754\) | 4.78775 | 0.174360 | ||||||||
\(755\) | 14.0000 | 0.509512 | ||||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | −25.6969 | −0.933971 | −0.466986 | − | 0.884265i | \(-0.654660\pi\) | ||||
−0.466986 | + | 0.884265i | \(0.654660\pi\) | |||||||
\(758\) | 81.7980 | 2.97104 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.20204 | 0.0798764 | ||||||||
\(761\) | −20.1464 | −0.730307 | −0.365154 | − | 0.930947i | \(-0.618984\pi\) | ||||
−0.365154 | + | 0.930947i | \(0.618984\pi\) | |||||||
\(762\) | −15.7980 | −0.572300 | ||||||||
\(763\) | −16.4495 | −0.595512 | ||||||||
\(764\) | −24.9898 | −0.904099 | ||||||||
\(765\) | 0.550510 | 0.0199037 | ||||||||
\(766\) | −40.0454 | −1.44690 | ||||||||
\(767\) | 1.95459 | 0.0705762 | ||||||||
\(768\) | −32.0000 | −1.15470 | ||||||||
\(769\) | −5.55051 | −0.200157 | −0.100078 | − | 0.994980i | \(-0.531909\pi\) | ||||
−0.100078 | + | 0.994980i | \(0.531909\pi\) | |||||||
\(770\) | 6.00000 | 0.216225 | ||||||||
\(771\) | −10.6515 | −0.383606 | ||||||||
\(772\) | 90.7878 | 3.26752 | ||||||||
\(773\) | −52.2929 | −1.88084 | −0.940422 | − | 0.340010i | \(-0.889569\pi\) | ||||
−0.940422 | + | 0.340010i | \(0.889569\pi\) | |||||||
\(774\) | −4.89898 | −0.176090 | ||||||||
\(775\) | 9.89898 | 0.355582 | ||||||||
\(776\) | −63.1918 | −2.26845 | ||||||||
\(777\) | 5.89898 | 0.211625 | ||||||||
\(778\) | 80.0908 | 2.87139 | ||||||||
\(779\) | 0.247449 | 0.00886577 | ||||||||
\(780\) | −1.79796 | −0.0643773 | ||||||||
\(781\) | 25.3485 | 0.907040 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.34847 | −0.155402 | ||||||||
\(784\) | −24.0000 | −0.857143 | ||||||||
\(785\) | 20.5959 | 0.735100 | ||||||||
\(786\) | 48.0000 | 1.71210 | ||||||||
\(787\) | −7.69694 | −0.274366 | −0.137183 | − | 0.990546i | \(-0.543805\pi\) | ||||
−0.137183 | + | 0.990546i | \(0.543805\pi\) | |||||||
\(788\) | −52.4041 | −1.86682 | ||||||||
\(789\) | −2.75255 | −0.0979934 | ||||||||
\(790\) | 9.79796 | 0.348596 | ||||||||
\(791\) | 16.3485 | 0.581285 | ||||||||
\(792\) | 12.0000 | 0.426401 | ||||||||
\(793\) | 6.89898 | 0.244990 | ||||||||
\(794\) | 14.2020 | 0.504012 | ||||||||
\(795\) | −5.44949 | −0.193273 | ||||||||
\(796\) | −27.5959 | −0.978111 | ||||||||
\(797\) | 15.2474 | 0.540092 | 0.270046 | − | 0.962847i | \(-0.412961\pi\) | ||||
0.270046 | + | 0.962847i | \(0.412961\pi\) | |||||||
\(798\) | 1.10102 | 0.0389757 | ||||||||
\(799\) | 1.95459 | 0.0691485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.10102 | 0.250902 | ||||||||
\(802\) | 56.0908 | 1.98064 | ||||||||
\(803\) | 22.8990 | 0.808087 | ||||||||
\(804\) | 28.0000 | 0.987484 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.8990 | −0.383900 | ||||||||
\(807\) | −0.550510 | −0.0193789 | ||||||||
\(808\) | −85.4847 | −3.00734 | ||||||||
\(809\) | 11.4495 | 0.402543 | 0.201271 | − | 0.979536i | \(-0.435493\pi\) | ||||
0.201271 | + | 0.979536i | \(0.435493\pi\) | |||||||
\(810\) | 2.44949 | 0.0860663 | ||||||||
\(811\) | 16.3939 | 0.575667 | 0.287833 | − | 0.957680i | \(-0.407065\pi\) | ||||
0.287833 | + | 0.957680i | \(0.407065\pi\) | |||||||
\(812\) | −17.3939 | −0.610405 | ||||||||
\(813\) | 2.30306 | 0.0807719 | ||||||||
\(814\) | 35.3939 | 1.24055 | ||||||||
\(815\) | −10.0000 | −0.350285 | ||||||||
\(816\) | 2.20204 | 0.0770869 | ||||||||
\(817\) | −0.898979 | −0.0314513 | ||||||||
\(818\) | 29.6413 | 1.03638 | ||||||||
\(819\) | −0.449490 | −0.0157064 | ||||||||
\(820\) | 2.20204 | 0.0768986 | ||||||||
\(821\) | 50.6969 | 1.76934 | 0.884668 | − | 0.466222i | \(-0.154385\pi\) | ||||
0.884668 | + | 0.466222i | \(0.154385\pi\) | |||||||
\(822\) | 17.3939 | 0.606681 | ||||||||
\(823\) | −35.5959 | −1.24080 | −0.620398 | − | 0.784287i | \(-0.713029\pi\) | ||||
−0.620398 | + | 0.784287i | \(0.713029\pi\) | |||||||
\(824\) | −81.7980 | −2.84957 | ||||||||
\(825\) | 2.44949 | 0.0852803 | ||||||||
\(826\) | −10.6515 | −0.370614 | ||||||||
\(827\) | 2.14643 | 0.0746386 | 0.0373193 | − | 0.999303i | \(-0.488118\pi\) | ||||
0.0373193 | + | 0.999303i | \(0.488118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.69694 | 0.0589371 | 0.0294686 | − | 0.999566i | \(-0.490619\pi\) | ||||
0.0294686 | + | 0.999566i | \(0.490619\pi\) | |||||||
\(830\) | 22.6515 | 0.786246 | ||||||||
\(831\) | −10.0000 | −0.346896 | ||||||||
\(832\) | 3.59592 | 0.124666 | ||||||||
\(833\) | −3.30306 | −0.114444 | ||||||||
\(834\) | 36.2474 | 1.25515 | ||||||||
\(835\) | −1.34847 | −0.0466657 | ||||||||
\(836\) | 4.40408 | 0.152318 | ||||||||
\(837\) | 9.89898 | 0.342159 | ||||||||
\(838\) | −94.1816 | −3.25345 | ||||||||
\(839\) | −33.1918 | −1.14591 | −0.572955 | − | 0.819587i | \(-0.694203\pi\) | ||||
−0.572955 | + | 0.819587i | \(0.694203\pi\) | |||||||
\(840\) | 4.89898 | 0.169031 | ||||||||
\(841\) | −10.0908 | −0.347959 | ||||||||
\(842\) | −5.50510 | −0.189718 | ||||||||
\(843\) | 4.65153 | 0.160207 | ||||||||
\(844\) | 44.0000 | 1.51454 | ||||||||
\(845\) | −12.7980 | −0.440263 | ||||||||
\(846\) | 8.69694 | 0.299007 | ||||||||
\(847\) | −5.00000 | −0.171802 | ||||||||
\(848\) | −21.7980 | −0.748545 | ||||||||
\(849\) | 11.8990 | 0.408372 | ||||||||
\(850\) | 1.34847 | 0.0462521 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 41.3939 | 1.41813 | ||||||||
\(853\) | −42.0908 | −1.44116 | −0.720581 | − | 0.693371i | \(-0.756125\pi\) | ||||
−0.720581 | + | 0.693371i | \(0.756125\pi\) | |||||||
\(854\) | −37.5959 | −1.28651 | ||||||||
\(855\) | 0.449490 | 0.0153722 | ||||||||
\(856\) | 2.69694 | 0.0921795 | ||||||||
\(857\) | 25.5959 | 0.874340 | 0.437170 | − | 0.899379i | \(-0.355981\pi\) | ||||
0.437170 | + | 0.899379i | \(0.355981\pi\) | |||||||
\(858\) | −2.69694 | −0.0920720 | ||||||||
\(859\) | −40.1918 | −1.37133 | −0.685664 | − | 0.727918i | \(-0.740488\pi\) | ||||
−0.685664 | + | 0.727918i | \(0.740488\pi\) | |||||||
\(860\) | −8.00000 | −0.272798 | ||||||||
\(861\) | 0.550510 | 0.0187613 | ||||||||
\(862\) | −60.0000 | −2.04361 | ||||||||
\(863\) | −42.4949 | −1.44654 | −0.723272 | − | 0.690564i | \(-0.757363\pi\) | ||||
−0.723272 | + | 0.690564i | \(0.757363\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.5959 | −0.666281 | ||||||||
\(866\) | 41.1464 | 1.39821 | ||||||||
\(867\) | −16.6969 | −0.567058 | ||||||||
\(868\) | 39.5959 | 1.34397 | ||||||||
\(869\) | 9.79796 | 0.332373 | ||||||||
\(870\) | −10.6515 | −0.361121 | ||||||||
\(871\) | −3.14643 | −0.106613 | ||||||||
\(872\) | −80.5857 | −2.72898 | ||||||||
\(873\) | −12.8990 | −0.436564 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 37.3939 | 1.26342 | ||||||||
\(877\) | 38.4949 | 1.29988 | 0.649940 | − | 0.759985i | \(-0.274794\pi\) | ||||
0.649940 | + | 0.759985i | \(0.274794\pi\) | |||||||
\(878\) | −17.8888 | −0.603717 | ||||||||
\(879\) | −3.24745 | −0.109534 | ||||||||
\(880\) | 9.79796 | 0.330289 | ||||||||
\(881\) | −3.55051 | −0.119620 | −0.0598099 | − | 0.998210i | \(-0.519049\pi\) | ||||
−0.0598099 | + | 0.998210i | \(0.519049\pi\) | |||||||
\(882\) | −14.6969 | −0.494872 | ||||||||
\(883\) | −42.4495 | −1.42854 | −0.714270 | − | 0.699871i | \(-0.753241\pi\) | ||||
−0.714270 | + | 0.699871i | \(0.753241\pi\) | |||||||
\(884\) | −0.989795 | −0.0332904 | ||||||||
\(885\) | −4.34847 | −0.146172 | ||||||||
\(886\) | −38.0908 | −1.27969 | ||||||||
\(887\) | 42.4949 | 1.42684 | 0.713420 | − | 0.700737i | \(-0.247145\pi\) | ||||
0.713420 | + | 0.700737i | \(0.247145\pi\) | |||||||
\(888\) | 28.8990 | 0.969786 | ||||||||
\(889\) | −6.44949 | −0.216309 | ||||||||
\(890\) | 17.3939 | 0.583044 | ||||||||
\(891\) | 2.44949 | 0.0820610 | ||||||||
\(892\) | −70.3837 | −2.35662 | ||||||||
\(893\) | 1.59592 | 0.0534054 | ||||||||
\(894\) | −32.6969 | −1.09355 | ||||||||
\(895\) | −6.00000 | −0.200558 | ||||||||
\(896\) | −19.5959 | −0.654654 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.95459 | 0.265448 | ||||||||
\(899\) | −43.0454 | −1.43564 | ||||||||
\(900\) | 4.00000 | 0.133333 | ||||||||
\(901\) | −3.00000 | −0.0999445 | ||||||||
\(902\) | 3.30306 | 0.109980 | ||||||||
\(903\) | −2.00000 | −0.0665558 | ||||||||
\(904\) | 80.0908 | 2.66378 | ||||||||
\(905\) | −0.898979 | −0.0298831 | ||||||||
\(906\) | 34.2929 | 1.13930 | ||||||||
\(907\) | −19.2020 | −0.637593 | −0.318797 | − | 0.947823i | \(-0.603279\pi\) | ||||
−0.318797 | + | 0.947823i | \(0.603279\pi\) | |||||||
\(908\) | −8.80816 | −0.292309 | ||||||||
\(909\) | −17.4495 | −0.578763 | ||||||||
\(910\) | −1.10102 | −0.0364985 | ||||||||
\(911\) | 33.7980 | 1.11978 | 0.559888 | − | 0.828568i | \(-0.310844\pi\) | ||||
0.559888 | + | 0.828568i | \(0.310844\pi\) | |||||||
\(912\) | 1.79796 | 0.0595364 | ||||||||
\(913\) | 22.6515 | 0.749656 | ||||||||
\(914\) | −24.2474 | −0.802034 | ||||||||
\(915\) | −15.3485 | −0.507405 | ||||||||
\(916\) | −81.9796 | −2.70868 | ||||||||
\(917\) | 19.5959 | 0.647114 | ||||||||
\(918\) | 1.34847 | 0.0445061 | ||||||||
\(919\) | −13.3939 | −0.441823 | −0.220912 | − | 0.975294i | \(-0.570903\pi\) | ||||
−0.220912 | + | 0.975294i | \(0.570903\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.3485 | −0.571651 | ||||||||
\(922\) | 74.6969 | 2.46001 | ||||||||
\(923\) | −4.65153 | −0.153107 | ||||||||
\(924\) | 9.79796 | 0.322329 | ||||||||
\(925\) | 5.89898 | 0.193957 | ||||||||
\(926\) | 70.8990 | 2.32989 | ||||||||
\(927\) | −16.6969 | −0.548399 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.8434 | −1.34003 | −0.670014 | − | 0.742349i | \(-0.733712\pi\) | ||||
−0.670014 | + | 0.742349i | \(0.733712\pi\) | |||||||
\(930\) | 24.2474 | 0.795105 | ||||||||
\(931\) | −2.69694 | −0.0883886 | ||||||||
\(932\) | 8.80816 | 0.288521 | ||||||||
\(933\) | 12.0000 | 0.392862 | ||||||||
\(934\) | −70.6515 | −2.31179 | ||||||||
\(935\) | 1.34847 | 0.0440997 | ||||||||
\(936\) | −2.20204 | −0.0719760 | ||||||||
\(937\) | −0.898979 | −0.0293684 | −0.0146842 | − | 0.999892i | \(-0.504674\pi\) | ||||
−0.0146842 | + | 0.999892i | \(0.504674\pi\) | |||||||
\(938\) | 17.1464 | 0.559851 | ||||||||
\(939\) | 9.69694 | 0.316448 | ||||||||
\(940\) | 14.2020 | 0.463220 | ||||||||
\(941\) | 59.1464 | 1.92812 | 0.964059 | − | 0.265687i | \(-0.0855989\pi\) | ||||
0.964059 | + | 0.265687i | \(0.0855989\pi\) | |||||||
\(942\) | 50.4495 | 1.64373 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −17.3939 | −0.566122 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | −12.0000 | −0.390154 | ||||||||
\(947\) | 48.4949 | 1.57587 | 0.787936 | − | 0.615757i | \(-0.211150\pi\) | ||||
0.787936 | + | 0.615757i | \(0.211150\pi\) | |||||||
\(948\) | 16.0000 | 0.519656 | ||||||||
\(949\) | −4.20204 | −0.136404 | ||||||||
\(950\) | 1.10102 | 0.0357218 | ||||||||
\(951\) | −18.2474 | −0.591714 | ||||||||
\(952\) | 2.69694 | 0.0874083 | ||||||||
\(953\) | −49.5959 | −1.60657 | −0.803285 | − | 0.595595i | \(-0.796916\pi\) | ||||
−0.803285 | + | 0.595595i | \(0.796916\pi\) | |||||||
\(954\) | −13.3485 | −0.432173 | ||||||||
\(955\) | −6.24745 | −0.202163 | ||||||||
\(956\) | 45.7980 | 1.48121 | ||||||||
\(957\) | −10.6515 | −0.344315 | ||||||||
\(958\) | 51.3031 | 1.65753 | ||||||||
\(959\) | 7.10102 | 0.229304 | ||||||||
\(960\) | −8.00000 | −0.258199 | ||||||||
\(961\) | 66.9898 | 2.16096 | ||||||||
\(962\) | −6.49490 | −0.209404 | ||||||||
\(963\) | 0.550510 | 0.0177399 | ||||||||
\(964\) | 58.6061 | 1.88758 | ||||||||
\(965\) | 22.6969 | 0.730640 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.95459 | 0.320118 | 0.160059 | − | 0.987107i | \(-0.448832\pi\) | ||||
0.160059 | + | 0.987107i | \(0.448832\pi\) | |||||||
\(968\) | −24.4949 | −0.787296 | ||||||||
\(969\) | 0.247449 | 0.00794920 | ||||||||
\(970\) | −31.5959 | −1.01448 | ||||||||
\(971\) | 46.2929 | 1.48561 | 0.742804 | − | 0.669509i | \(-0.233495\pi\) | ||||
0.742804 | + | 0.669509i | \(0.233495\pi\) | |||||||
\(972\) | 4.00000 | 0.128300 | ||||||||
\(973\) | 14.7980 | 0.474401 | ||||||||
\(974\) | 85.5959 | 2.74267 | ||||||||
\(975\) | −0.449490 | −0.0143952 | ||||||||
\(976\) | −61.3939 | −1.96517 | ||||||||
\(977\) | −34.3485 | −1.09890 | −0.549452 | − | 0.835525i | \(-0.685164\pi\) | ||||
−0.549452 | + | 0.835525i | \(0.685164\pi\) | |||||||
\(978\) | −24.4949 | −0.783260 | ||||||||
\(979\) | 17.3939 | 0.555911 | ||||||||
\(980\) | −24.0000 | −0.766652 | ||||||||
\(981\) | −16.4495 | −0.525192 | ||||||||
\(982\) | 42.7423 | 1.36396 | ||||||||
\(983\) | −39.7423 | −1.26758 | −0.633792 | − | 0.773504i | \(-0.718502\pi\) | ||||
−0.633792 | + | 0.773504i | \(0.718502\pi\) | |||||||
\(984\) | 2.69694 | 0.0859753 | ||||||||
\(985\) | −13.1010 | −0.417433 | ||||||||
\(986\) | −5.86378 | −0.186741 | ||||||||
\(987\) | 3.55051 | 0.113014 | ||||||||
\(988\) | −0.808164 | −0.0257111 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 6.00000 | 0.190693 | ||||||||
\(991\) | −59.7878 | −1.89922 | −0.949610 | − | 0.313433i | \(-0.898521\pi\) | ||||
−0.949610 | + | 0.313433i | \(0.898521\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.5959 | −0.463187 | ||||||||
\(994\) | 25.3485 | 0.804005 | ||||||||
\(995\) | −6.89898 | −0.218712 | ||||||||
\(996\) | 36.9898 | 1.17207 | ||||||||
\(997\) | −48.0908 | −1.52305 | −0.761526 | − | 0.648135i | \(-0.775549\pi\) | ||||
−0.761526 | + | 0.648135i | \(0.775549\pi\) | |||||||
\(998\) | −2.44949 | −0.0775372 | ||||||||
\(999\) | 5.89898 | 0.186635 |
(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 | 7935.2.a.t.1.2 | 2 | ||
23.22 | odd | 2 | 345.2.a.i.1.2 | ✓ | 2 | ||
69.68 | even | 2 | 1035.2.a.k.1.1 | 2 | |||
92.91 | even | 2 | 5520.2.a.bi.1.2 | 2 | |||
115.22 | even | 4 | 1725.2.b.m.1174.3 | 4 | |||
115.68 | even | 4 | 1725.2.b.m.1174.2 | 4 | |||
115.114 | odd | 2 | 1725.2.a.y.1.1 | 2 | |||
345.344 | even | 2 | 5175.2.a.bl.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
345.2.a.i.1.2 | ✓ | 2 | 23.22 | odd | 2 | ||
1035.2.a.k.1.1 | 2 | 69.68 | even | 2 | |||
1725.2.a.y.1.1 | 2 | 115.114 | odd | 2 | |||
1725.2.b.m.1174.2 | 4 | 115.68 | even | 4 | |||
1725.2.b.m.1174.3 | 4 | 115.22 | even | 4 | |||
5175.2.a.bl.1.2 | 2 | 345.344 | even | 2 | |||
5520.2.a.bi.1.2 | 2 | 92.91 | even | 2 | |||
7935.2.a.t.1.2 | 2 | 1.1 | even | 1 | trivial |