Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.6148961.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 11x^{4} + 12x^{3} + 32x^{2} - 16x - 29 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.58604\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.59594 | 1.16094 | 0.580470 | − | 0.814282i | \(-0.302869\pi\) | ||||
0.580470 | + | 0.814282i | \(0.302869\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.59594 | 0.820908 | ||||||||
\(11\) | 5.12317 | 1.54469 | 0.772347 | − | 0.635201i | \(-0.219083\pi\) | ||||
0.772347 | + | 0.635201i | \(0.219083\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 2.59594 | 0.670269 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.39467 | −0.823328 | −0.411664 | − | 0.911336i | \(-0.635052\pi\) | ||||
−0.411664 | + | 0.911336i | \(0.635052\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.0178327 | 0.00409110 | 0.00204555 | − | 0.999998i | \(-0.499349\pi\) | ||||
0.00204555 | + | 0.999998i | \(0.499349\pi\) | |||||||
\(20\) | 2.59594 | 0.580470 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 5.12317 | 1.09226 | ||||||||
\(23\) | 7.09063 | 1.47850 | 0.739249 | − | 0.673432i | \(-0.235181\pi\) | ||||
0.739249 | + | 0.673432i | \(0.235181\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.73890 | 0.347780 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 4.27806 | 0.794417 | 0.397208 | − | 0.917728i | \(-0.369979\pi\) | ||||
0.397208 | + | 0.917728i | \(0.369979\pi\) | |||||||
\(30\) | 2.59594 | 0.473951 | ||||||||
\(31\) | −0.430922 | −0.0773958 | −0.0386979 | − | 0.999251i | \(-0.512321\pi\) | ||||
−0.0386979 | + | 0.999251i | \(0.512321\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.12317 | 0.891829 | ||||||||
\(34\) | −3.39467 | −0.582181 | ||||||||
\(35\) | −2.59594 | −0.438794 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.46183 | −0.733520 | −0.366760 | − | 0.930316i | \(-0.619533\pi\) | ||||
−0.366760 | + | 0.930316i | \(0.619533\pi\) | |||||||
\(38\) | 0.0178327 | 0.00289285 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.59594 | 0.410454 | ||||||||
\(41\) | 2.69358 | 0.420666 | 0.210333 | − | 0.977630i | \(-0.432545\pi\) | ||||
0.210333 | + | 0.977630i | \(0.432545\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 11.1823 | 1.70529 | 0.852643 | − | 0.522494i | \(-0.174998\pi\) | ||||
0.852643 | + | 0.522494i | \(0.174998\pi\) | |||||||
\(44\) | 5.12317 | 0.772347 | ||||||||
\(45\) | 2.59594 | 0.386980 | ||||||||
\(46\) | 7.09063 | 1.04546 | ||||||||
\(47\) | −5.56996 | −0.812463 | −0.406231 | − | 0.913770i | \(-0.633157\pi\) | ||||
−0.406231 | + | 0.913770i | \(0.633157\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.73890 | 0.245918 | ||||||||
\(51\) | −3.39467 | −0.475349 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.44524 | −1.29740 | −0.648702 | − | 0.761043i | \(-0.724688\pi\) | ||||
−0.648702 | + | 0.761043i | \(0.724688\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 13.2994 | 1.79330 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0.0178327 | 0.00236200 | ||||||||
\(58\) | 4.27806 | 0.561737 | ||||||||
\(59\) | −13.2304 | −1.72245 | −0.861223 | − | 0.508228i | \(-0.830301\pi\) | ||||
−0.861223 | + | 0.508228i | \(0.830301\pi\) | |||||||
\(60\) | 2.59594 | 0.335134 | ||||||||
\(61\) | −7.25936 | −0.929466 | −0.464733 | − | 0.885451i | \(-0.653850\pi\) | ||||
−0.464733 | + | 0.885451i | \(0.653850\pi\) | |||||||
\(62\) | −0.430922 | −0.0547271 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.12317 | 0.630618 | ||||||||
\(67\) | −1.37917 | −0.168493 | −0.0842463 | − | 0.996445i | \(-0.526848\pi\) | ||||
−0.0842463 | + | 0.996445i | \(0.526848\pi\) | |||||||
\(68\) | −3.39467 | −0.411664 | ||||||||
\(69\) | 7.09063 | 0.853611 | ||||||||
\(70\) | −2.59594 | −0.310274 | ||||||||
\(71\) | 12.7469 | 1.51278 | 0.756390 | − | 0.654121i | \(-0.226961\pi\) | ||||
0.756390 | + | 0.654121i | \(0.226961\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −3.14421 | −0.368002 | −0.184001 | − | 0.982926i | \(-0.558905\pi\) | ||||
−0.184001 | + | 0.982926i | \(0.558905\pi\) | |||||||
\(74\) | −4.46183 | −0.518677 | ||||||||
\(75\) | 1.73890 | 0.200791 | ||||||||
\(76\) | 0.0178327 | 0.00204555 | ||||||||
\(77\) | −5.12317 | −0.583839 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.29899 | 0.821201 | 0.410600 | − | 0.911815i | \(-0.365319\pi\) | ||||
0.410600 | + | 0.911815i | \(0.365319\pi\) | |||||||
\(80\) | 2.59594 | 0.290235 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.69358 | 0.297456 | ||||||||
\(83\) | 2.41028 | 0.264563 | 0.132282 | − | 0.991212i | \(-0.457770\pi\) | ||||
0.132282 | + | 0.991212i | \(0.457770\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −8.81236 | −0.955834 | ||||||||
\(86\) | 11.1823 | 1.20582 | ||||||||
\(87\) | 4.27806 | 0.458657 | ||||||||
\(88\) | 5.12317 | 0.546132 | ||||||||
\(89\) | −2.71911 | −0.288225 | −0.144112 | − | 0.989561i | \(-0.546033\pi\) | ||||
−0.144112 | + | 0.989561i | \(0.546033\pi\) | |||||||
\(90\) | 2.59594 | 0.273636 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.09063 | 0.739249 | ||||||||
\(93\) | −0.430922 | −0.0446845 | ||||||||
\(94\) | −5.56996 | −0.574498 | ||||||||
\(95\) | 0.0462926 | 0.00474952 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 16.7222 | 1.69788 | 0.848941 | − | 0.528487i | \(-0.177240\pi\) | ||||
0.848941 | + | 0.528487i | \(0.177240\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 5.12317 | 0.514898 | ||||||||
\(100\) | 1.73890 | 0.173890 | ||||||||
\(101\) | −13.7189 | −1.36508 | −0.682538 | − | 0.730850i | \(-0.739124\pi\) | ||||
−0.682538 | + | 0.730850i | \(0.739124\pi\) | |||||||
\(102\) | −3.39467 | −0.336122 | ||||||||
\(103\) | 4.24896 | 0.418662 | 0.209331 | − | 0.977845i | \(-0.432871\pi\) | ||||
0.209331 | + | 0.977845i | \(0.432871\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.59594 | −0.253338 | ||||||||
\(106\) | −9.44524 | −0.917403 | ||||||||
\(107\) | −2.43068 | −0.234983 | −0.117491 | − | 0.993074i | \(-0.537485\pi\) | ||||
−0.117491 | + | 0.993074i | \(0.537485\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 10.8152 | 1.03591 | 0.517956 | − | 0.855408i | \(-0.326693\pi\) | ||||
0.517956 | + | 0.855408i | \(0.326693\pi\) | |||||||
\(110\) | 13.2994 | 1.26805 | ||||||||
\(111\) | −4.46183 | −0.423498 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −1.94348 | −0.182827 | −0.0914137 | − | 0.995813i | \(-0.529139\pi\) | ||||
−0.0914137 | + | 0.995813i | \(0.529139\pi\) | |||||||
\(114\) | 0.0178327 | 0.00167019 | ||||||||
\(115\) | 18.4068 | 1.71645 | ||||||||
\(116\) | 4.27806 | 0.397208 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.2304 | −1.21795 | ||||||||
\(119\) | 3.39467 | 0.311189 | ||||||||
\(120\) | 2.59594 | 0.236976 | ||||||||
\(121\) | 15.2469 | 1.38608 | ||||||||
\(122\) | −7.25936 | −0.657232 | ||||||||
\(123\) | 2.69358 | 0.242872 | ||||||||
\(124\) | −0.430922 | −0.0386979 | ||||||||
\(125\) | −8.46562 | −0.757188 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −10.1063 | −0.896787 | −0.448394 | − | 0.893836i | \(-0.648004\pi\) | ||||
−0.448394 | + | 0.893836i | \(0.648004\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 11.1823 | 0.984547 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.1622 | −1.41210 | −0.706049 | − | 0.708163i | \(-0.749524\pi\) | ||||
−0.706049 | + | 0.708163i | \(0.749524\pi\) | |||||||
\(132\) | 5.12317 | 0.445915 | ||||||||
\(133\) | −0.0178327 | −0.00154629 | ||||||||
\(134\) | −1.37917 | −0.119142 | ||||||||
\(135\) | 2.59594 | 0.223423 | ||||||||
\(136\) | −3.39467 | −0.291091 | ||||||||
\(137\) | 11.6110 | 0.991994 | 0.495997 | − | 0.868324i | \(-0.334803\pi\) | ||||
0.495997 | + | 0.868324i | \(0.334803\pi\) | |||||||
\(138\) | 7.09063 | 0.603594 | ||||||||
\(139\) | −9.39315 | −0.796716 | −0.398358 | − | 0.917230i | \(-0.630420\pi\) | ||||
−0.398358 | + | 0.917230i | \(0.630420\pi\) | |||||||
\(140\) | −2.59594 | −0.219397 | ||||||||
\(141\) | −5.56996 | −0.469075 | ||||||||
\(142\) | 12.7469 | 1.06970 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 11.1056 | 0.922269 | ||||||||
\(146\) | −3.14421 | −0.260216 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −4.46183 | −0.366760 | ||||||||
\(149\) | 17.9543 | 1.47088 | 0.735438 | − | 0.677592i | \(-0.236976\pi\) | ||||
0.735438 | + | 0.677592i | \(0.236976\pi\) | |||||||
\(150\) | 1.73890 | 0.141981 | ||||||||
\(151\) | 5.67926 | 0.462172 | 0.231086 | − | 0.972933i | \(-0.425772\pi\) | ||||
0.231086 | + | 0.972933i | \(0.425772\pi\) | |||||||
\(152\) | 0.0178327 | 0.00144642 | ||||||||
\(153\) | −3.39467 | −0.274443 | ||||||||
\(154\) | −5.12317 | −0.412837 | ||||||||
\(155\) | −1.11865 | −0.0898518 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.36185 | 0.747157 | 0.373579 | − | 0.927598i | \(-0.378131\pi\) | ||||
0.373579 | + | 0.927598i | \(0.378131\pi\) | |||||||
\(158\) | 7.29899 | 0.580677 | ||||||||
\(159\) | −9.44524 | −0.749056 | ||||||||
\(160\) | 2.59594 | 0.205227 | ||||||||
\(161\) | −7.09063 | −0.558820 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −15.9019 | −1.24553 | −0.622767 | − | 0.782407i | \(-0.713992\pi\) | ||||
−0.622767 | + | 0.782407i | \(0.713992\pi\) | |||||||
\(164\) | 2.69358 | 0.210333 | ||||||||
\(165\) | 13.2994 | 1.03536 | ||||||||
\(166\) | 2.41028 | 0.187074 | ||||||||
\(167\) | 22.9624 | 1.77688 | 0.888441 | − | 0.458990i | \(-0.151789\pi\) | ||||
0.888441 | + | 0.458990i | \(0.151789\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8.81236 | −0.675877 | ||||||||
\(171\) | 0.0178327 | 0.00136370 | ||||||||
\(172\) | 11.1823 | 0.852643 | ||||||||
\(173\) | −13.2994 | −1.01114 | −0.505568 | − | 0.862787i | \(-0.668717\pi\) | ||||
−0.505568 | + | 0.862787i | \(0.668717\pi\) | |||||||
\(174\) | 4.27806 | 0.324319 | ||||||||
\(175\) | −1.73890 | −0.131448 | ||||||||
\(176\) | 5.12317 | 0.386173 | ||||||||
\(177\) | −13.2304 | −0.994454 | ||||||||
\(178\) | −2.71911 | −0.203806 | ||||||||
\(179\) | 11.1476 | 0.833213 | 0.416607 | − | 0.909087i | \(-0.363219\pi\) | ||||
0.416607 | + | 0.909087i | \(0.363219\pi\) | |||||||
\(180\) | 2.59594 | 0.193490 | ||||||||
\(181\) | −18.9951 | −1.41189 | −0.705947 | − | 0.708264i | \(-0.749479\pi\) | ||||
−0.705947 | + | 0.708264i | \(0.749479\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.25936 | −0.536627 | ||||||||
\(184\) | 7.09063 | 0.522728 | ||||||||
\(185\) | −11.5826 | −0.851572 | ||||||||
\(186\) | −0.430922 | −0.0315967 | ||||||||
\(187\) | −17.3915 | −1.27179 | ||||||||
\(188\) | −5.56996 | −0.406231 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0.0462926 | 0.00335842 | ||||||||
\(191\) | −24.1986 | −1.75095 | −0.875475 | − | 0.483263i | \(-0.839452\pi\) | ||||
−0.875475 | + | 0.483263i | \(0.839452\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −10.8065 | −0.777871 | −0.388936 | − | 0.921265i | \(-0.627157\pi\) | ||||
−0.388936 | + | 0.921265i | \(0.627157\pi\) | |||||||
\(194\) | 16.7222 | 1.20058 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −2.43849 | −0.173735 | −0.0868677 | − | 0.996220i | \(-0.527686\pi\) | ||||
−0.0868677 | + | 0.996220i | \(0.527686\pi\) | |||||||
\(198\) | 5.12317 | 0.364088 | ||||||||
\(199\) | 18.5328 | 1.31375 | 0.656877 | − | 0.753997i | \(-0.271877\pi\) | ||||
0.656877 | + | 0.753997i | \(0.271877\pi\) | |||||||
\(200\) | 1.73890 | 0.122959 | ||||||||
\(201\) | −1.37917 | −0.0972793 | ||||||||
\(202\) | −13.7189 | −0.965255 | ||||||||
\(203\) | −4.27806 | −0.300261 | ||||||||
\(204\) | −3.39467 | −0.237674 | ||||||||
\(205\) | 6.99236 | 0.488368 | ||||||||
\(206\) | 4.24896 | 0.296039 | ||||||||
\(207\) | 7.09063 | 0.492833 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0913600 | 0.00631950 | ||||||||
\(210\) | −2.59594 | −0.179137 | ||||||||
\(211\) | −6.21752 | −0.428032 | −0.214016 | − | 0.976830i | \(-0.568654\pi\) | ||||
−0.214016 | + | 0.976830i | \(0.568654\pi\) | |||||||
\(212\) | −9.44524 | −0.648702 | ||||||||
\(213\) | 12.7469 | 0.873404 | ||||||||
\(214\) | −2.43068 | −0.166158 | ||||||||
\(215\) | 29.0286 | 1.97973 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0.430922 | 0.0292529 | ||||||||
\(218\) | 10.8152 | 0.732500 | ||||||||
\(219\) | −3.14421 | −0.212466 | ||||||||
\(220\) | 13.2994 | 0.896648 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.46183 | −0.299458 | ||||||||
\(223\) | 19.3445 | 1.29540 | 0.647702 | − | 0.761894i | \(-0.275730\pi\) | ||||
0.647702 | + | 0.761894i | \(0.275730\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 1.73890 | 0.115927 | ||||||||
\(226\) | −1.94348 | −0.129278 | ||||||||
\(227\) | 9.78761 | 0.649626 | 0.324813 | − | 0.945778i | \(-0.394699\pi\) | ||||
0.324813 | + | 0.945778i | \(0.394699\pi\) | |||||||
\(228\) | 0.0178327 | 0.00118100 | ||||||||
\(229\) | −7.53482 | −0.497915 | −0.248957 | − | 0.968514i | \(-0.580088\pi\) | ||||
−0.248957 | + | 0.968514i | \(0.580088\pi\) | |||||||
\(230\) | 18.4068 | 1.21371 | ||||||||
\(231\) | −5.12317 | −0.337080 | ||||||||
\(232\) | 4.27806 | 0.280869 | ||||||||
\(233\) | 29.4092 | 1.92666 | 0.963329 | − | 0.268323i | \(-0.0864694\pi\) | ||||
0.963329 | + | 0.268323i | \(0.0864694\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.4593 | −0.943220 | ||||||||
\(236\) | −13.2304 | −0.861223 | ||||||||
\(237\) | 7.29899 | 0.474121 | ||||||||
\(238\) | 3.39467 | 0.220044 | ||||||||
\(239\) | −26.1127 | −1.68909 | −0.844546 | − | 0.535483i | \(-0.820130\pi\) | ||||
−0.844546 | + | 0.535483i | \(0.820130\pi\) | |||||||
\(240\) | 2.59594 | 0.167567 | ||||||||
\(241\) | −1.71173 | −0.110262 | −0.0551312 | − | 0.998479i | \(-0.517558\pi\) | ||||
−0.0551312 | + | 0.998479i | \(0.517558\pi\) | |||||||
\(242\) | 15.2469 | 0.980105 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −7.25936 | −0.464733 | ||||||||
\(245\) | 2.59594 | 0.165848 | ||||||||
\(246\) | 2.69358 | 0.171736 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.430922 | −0.0273636 | ||||||||
\(249\) | 2.41028 | 0.152746 | ||||||||
\(250\) | −8.46562 | −0.535413 | ||||||||
\(251\) | −16.7525 | −1.05741 | −0.528705 | − | 0.848806i | \(-0.677322\pi\) | ||||
−0.528705 | + | 0.848806i | \(0.677322\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 36.3265 | 2.28383 | ||||||||
\(254\) | −10.1063 | −0.634124 | ||||||||
\(255\) | −8.81236 | −0.551851 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.6283 | −0.912489 | −0.456244 | − | 0.889854i | \(-0.650806\pi\) | ||||
−0.456244 | + | 0.889854i | \(0.650806\pi\) | |||||||
\(258\) | 11.1823 | 0.696180 | ||||||||
\(259\) | 4.46183 | 0.277244 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.27806 | 0.264806 | ||||||||
\(262\) | −16.1622 | −0.998503 | ||||||||
\(263\) | 17.3602 | 1.07047 | 0.535236 | − | 0.844702i | \(-0.320223\pi\) | ||||
0.535236 | + | 0.844702i | \(0.320223\pi\) | |||||||
\(264\) | 5.12317 | 0.315309 | ||||||||
\(265\) | −24.5193 | −1.50621 | ||||||||
\(266\) | −0.0178327 | −0.00109339 | ||||||||
\(267\) | −2.71911 | −0.166407 | ||||||||
\(268\) | −1.37917 | −0.0842463 | ||||||||
\(269\) | −7.43931 | −0.453583 | −0.226791 | − | 0.973943i | \(-0.572824\pi\) | ||||
−0.226791 | + | 0.973943i | \(0.572824\pi\) | |||||||
\(270\) | 2.59594 | 0.157984 | ||||||||
\(271\) | 11.3773 | 0.691119 | 0.345560 | − | 0.938397i | \(-0.387689\pi\) | ||||
0.345560 | + | 0.938397i | \(0.387689\pi\) | |||||||
\(272\) | −3.39467 | −0.205832 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.6110 | 0.701445 | ||||||||
\(275\) | 8.90868 | 0.537213 | ||||||||
\(276\) | 7.09063 | 0.426806 | ||||||||
\(277\) | −7.53314 | −0.452622 | −0.226311 | − | 0.974055i | \(-0.572667\pi\) | ||||
−0.226311 | + | 0.974055i | \(0.572667\pi\) | |||||||
\(278\) | −9.39315 | −0.563364 | ||||||||
\(279\) | −0.430922 | −0.0257986 | ||||||||
\(280\) | −2.59594 | −0.155137 | ||||||||
\(281\) | −7.32324 | −0.436868 | −0.218434 | − | 0.975852i | \(-0.570095\pi\) | ||||
−0.218434 | + | 0.975852i | \(0.570095\pi\) | |||||||
\(282\) | −5.56996 | −0.331686 | ||||||||
\(283\) | −12.5399 | −0.745419 | −0.372709 | − | 0.927948i | \(-0.621571\pi\) | ||||
−0.372709 | + | 0.927948i | \(0.621571\pi\) | |||||||
\(284\) | 12.7469 | 0.756390 | ||||||||
\(285\) | 0.0462926 | 0.00274214 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.69358 | −0.158997 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −5.47621 | −0.322130 | ||||||||
\(290\) | 11.1056 | 0.652143 | ||||||||
\(291\) | 16.7222 | 0.980273 | ||||||||
\(292\) | −3.14421 | −0.184001 | ||||||||
\(293\) | 19.0614 | 1.11358 | 0.556791 | − | 0.830653i | \(-0.312033\pi\) | ||||
0.556791 | + | 0.830653i | \(0.312033\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | −34.3452 | −1.99965 | ||||||||
\(296\) | −4.46183 | −0.259338 | ||||||||
\(297\) | 5.12317 | 0.297276 | ||||||||
\(298\) | 17.9543 | 1.04007 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.73890 | 0.100395 | ||||||||
\(301\) | −11.1823 | −0.644537 | ||||||||
\(302\) | 5.67926 | 0.326805 | ||||||||
\(303\) | −13.7189 | −0.788127 | ||||||||
\(304\) | 0.0178327 | 0.00102278 | ||||||||
\(305\) | −18.8449 | −1.07905 | ||||||||
\(306\) | −3.39467 | −0.194060 | ||||||||
\(307\) | −24.8387 | −1.41762 | −0.708809 | − | 0.705401i | \(-0.750767\pi\) | ||||
−0.708809 | + | 0.705401i | \(0.750767\pi\) | |||||||
\(308\) | −5.12317 | −0.291920 | ||||||||
\(309\) | 4.24896 | 0.241715 | ||||||||
\(310\) | −1.11865 | −0.0635348 | ||||||||
\(311\) | −0.438633 | −0.0248726 | −0.0124363 | − | 0.999923i | \(-0.503959\pi\) | ||||
−0.0124363 | + | 0.999923i | \(0.503959\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.3187 | 0.922390 | 0.461195 | − | 0.887299i | \(-0.347421\pi\) | ||||
0.461195 | + | 0.887299i | \(0.347421\pi\) | |||||||
\(314\) | 9.36185 | 0.528320 | ||||||||
\(315\) | −2.59594 | −0.146265 | ||||||||
\(316\) | 7.29899 | 0.410600 | ||||||||
\(317\) | −33.7161 | −1.89368 | −0.946841 | − | 0.321701i | \(-0.895746\pi\) | ||||
−0.946841 | + | 0.321701i | \(0.895746\pi\) | |||||||
\(318\) | −9.44524 | −0.529663 | ||||||||
\(319\) | 21.9172 | 1.22713 | ||||||||
\(320\) | 2.59594 | 0.145117 | ||||||||
\(321\) | −2.43068 | −0.135667 | ||||||||
\(322\) | −7.09063 | −0.395145 | ||||||||
\(323\) | −0.0605362 | −0.00336832 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.9019 | −0.880725 | ||||||||
\(327\) | 10.8152 | 0.598084 | ||||||||
\(328\) | 2.69358 | 0.148728 | ||||||||
\(329\) | 5.56996 | 0.307082 | ||||||||
\(330\) | 13.2994 | 0.732110 | ||||||||
\(331\) | 10.8454 | 0.596120 | 0.298060 | − | 0.954547i | \(-0.403661\pi\) | ||||
0.298060 | + | 0.954547i | \(0.403661\pi\) | |||||||
\(332\) | 2.41028 | 0.132282 | ||||||||
\(333\) | −4.46183 | −0.244507 | ||||||||
\(334\) | 22.9624 | 1.25645 | ||||||||
\(335\) | −3.58025 | −0.195610 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | −8.64433 | −0.470887 | −0.235443 | − | 0.971888i | \(-0.575654\pi\) | ||||
−0.235443 | + | 0.971888i | \(0.575654\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.94348 | −0.105555 | ||||||||
\(340\) | −8.81236 | −0.477917 | ||||||||
\(341\) | −2.20768 | −0.119553 | ||||||||
\(342\) | 0.0178327 | 0.000964283 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 11.1823 | 0.602910 | ||||||||
\(345\) | 18.4068 | 0.990991 | ||||||||
\(346\) | −13.2994 | −0.714981 | ||||||||
\(347\) | −24.0533 | −1.29125 | −0.645624 | − | 0.763655i | \(-0.723403\pi\) | ||||
−0.645624 | + | 0.763655i | \(0.723403\pi\) | |||||||
\(348\) | 4.27806 | 0.229328 | ||||||||
\(349\) | 31.3486 | 1.67805 | 0.839025 | − | 0.544092i | \(-0.183126\pi\) | ||||
0.839025 | + | 0.544092i | \(0.183126\pi\) | |||||||
\(350\) | −1.73890 | −0.0929481 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.12317 | 0.273066 | ||||||||
\(353\) | 11.8086 | 0.628508 | 0.314254 | − | 0.949339i | \(-0.398246\pi\) | ||||
0.314254 | + | 0.949339i | \(0.398246\pi\) | |||||||
\(354\) | −13.2304 | −0.703185 | ||||||||
\(355\) | 33.0902 | 1.75625 | ||||||||
\(356\) | −2.71911 | −0.144112 | ||||||||
\(357\) | 3.39467 | 0.179665 | ||||||||
\(358\) | 11.1476 | 0.589171 | ||||||||
\(359\) | 10.2791 | 0.542510 | 0.271255 | − | 0.962508i | \(-0.412561\pi\) | ||||
0.271255 | + | 0.962508i | \(0.412561\pi\) | |||||||
\(360\) | 2.59594 | 0.136818 | ||||||||
\(361\) | −18.9997 | −0.999983 | ||||||||
\(362\) | −18.9951 | −0.998360 | ||||||||
\(363\) | 15.2469 | 0.800252 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.16217 | −0.427228 | ||||||||
\(366\) | −7.25936 | −0.379453 | ||||||||
\(367\) | 23.8024 | 1.24248 | 0.621238 | − | 0.783622i | \(-0.286630\pi\) | ||||
0.621238 | + | 0.783622i | \(0.286630\pi\) | |||||||
\(368\) | 7.09063 | 0.369625 | ||||||||
\(369\) | 2.69358 | 0.140222 | ||||||||
\(370\) | −11.5826 | −0.602152 | ||||||||
\(371\) | 9.44524 | 0.490372 | ||||||||
\(372\) | −0.430922 | −0.0223422 | ||||||||
\(373\) | 4.82143 | 0.249644 | 0.124822 | − | 0.992179i | \(-0.460164\pi\) | ||||
0.124822 | + | 0.992179i | \(0.460164\pi\) | |||||||
\(374\) | −17.3915 | −0.899291 | ||||||||
\(375\) | −8.46562 | −0.437163 | ||||||||
\(376\) | −5.56996 | −0.287249 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 21.2547 | 1.09178 | 0.545892 | − | 0.837856i | \(-0.316191\pi\) | ||||
0.545892 | + | 0.837856i | \(0.316191\pi\) | |||||||
\(380\) | 0.0462926 | 0.00237476 | ||||||||
\(381\) | −10.1063 | −0.517760 | ||||||||
\(382\) | −24.1986 | −1.23811 | ||||||||
\(383\) | −32.6499 | −1.66833 | −0.834165 | − | 0.551515i | \(-0.814050\pi\) | ||||
−0.834165 | + | 0.551515i | \(0.814050\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −13.2994 | −0.677802 | ||||||||
\(386\) | −10.8065 | −0.550038 | ||||||||
\(387\) | 11.1823 | 0.568429 | ||||||||
\(388\) | 16.7222 | 0.848941 | ||||||||
\(389\) | −14.8469 | −0.752769 | −0.376385 | − | 0.926464i | \(-0.622833\pi\) | ||||
−0.376385 | + | 0.926464i | \(0.622833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0703 | −1.21729 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −16.1622 | −0.815275 | ||||||||
\(394\) | −2.43849 | −0.122849 | ||||||||
\(395\) | 18.9477 | 0.953364 | ||||||||
\(396\) | 5.12317 | 0.257449 | ||||||||
\(397\) | 15.5132 | 0.778583 | 0.389292 | − | 0.921115i | \(-0.372720\pi\) | ||||
0.389292 | + | 0.921115i | \(0.372720\pi\) | |||||||
\(398\) | 18.5328 | 0.928965 | ||||||||
\(399\) | −0.0178327 | −0.000892752 0 | ||||||||
\(400\) | 1.73890 | 0.0869450 | ||||||||
\(401\) | 11.1698 | 0.557792 | 0.278896 | − | 0.960321i | \(-0.410032\pi\) | ||||
0.278896 | + | 0.960321i | \(0.410032\pi\) | |||||||
\(402\) | −1.37917 | −0.0687868 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −13.7189 | −0.682538 | ||||||||
\(405\) | 2.59594 | 0.128993 | ||||||||
\(406\) | −4.27806 | −0.212317 | ||||||||
\(407\) | −22.8587 | −1.13306 | ||||||||
\(408\) | −3.39467 | −0.168061 | ||||||||
\(409\) | −1.82157 | −0.0900709 | −0.0450355 | − | 0.998985i | \(-0.514340\pi\) | ||||
−0.0450355 | + | 0.998985i | \(0.514340\pi\) | |||||||
\(410\) | 6.99236 | 0.345328 | ||||||||
\(411\) | 11.6110 | 0.572728 | ||||||||
\(412\) | 4.24896 | 0.209331 | ||||||||
\(413\) | 13.2304 | 0.651023 | ||||||||
\(414\) | 7.09063 | 0.348485 | ||||||||
\(415\) | 6.25695 | 0.307142 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.39315 | −0.459984 | ||||||||
\(418\) | 0.0913600 | 0.00446856 | ||||||||
\(419\) | 30.1385 | 1.47236 | 0.736182 | − | 0.676784i | \(-0.236627\pi\) | ||||
0.736182 | + | 0.676784i | \(0.236627\pi\) | |||||||
\(420\) | −2.59594 | −0.126669 | ||||||||
\(421\) | 17.7000 | 0.862645 | 0.431322 | − | 0.902198i | \(-0.358047\pi\) | ||||
0.431322 | + | 0.902198i | \(0.358047\pi\) | |||||||
\(422\) | −6.21752 | −0.302664 | ||||||||
\(423\) | −5.56996 | −0.270821 | ||||||||
\(424\) | −9.44524 | −0.458701 | ||||||||
\(425\) | −5.90299 | −0.286337 | ||||||||
\(426\) | 12.7469 | 0.617590 | ||||||||
\(427\) | 7.25936 | 0.351305 | ||||||||
\(428\) | −2.43068 | −0.117491 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 29.0286 | 1.39988 | ||||||||
\(431\) | −27.9368 | −1.34567 | −0.672834 | − | 0.739794i | \(-0.734923\pi\) | ||||
−0.672834 | + | 0.739794i | \(0.734923\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −26.1856 | −1.25840 | −0.629200 | − | 0.777243i | \(-0.716617\pi\) | ||||
−0.629200 | + | 0.777243i | \(0.716617\pi\) | |||||||
\(434\) | 0.430922 | 0.0206849 | ||||||||
\(435\) | 11.1056 | 0.532473 | ||||||||
\(436\) | 10.8152 | 0.517956 | ||||||||
\(437\) | 0.126445 | 0.00604869 | ||||||||
\(438\) | −3.14421 | −0.150236 | ||||||||
\(439\) | 7.29808 | 0.348318 | 0.174159 | − | 0.984718i | \(-0.444279\pi\) | ||||
0.174159 | + | 0.984718i | \(0.444279\pi\) | |||||||
\(440\) | 13.2994 | 0.634026 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0853 | −0.574190 | −0.287095 | − | 0.957902i | \(-0.592690\pi\) | ||||
−0.287095 | + | 0.957902i | \(0.592690\pi\) | |||||||
\(444\) | −4.46183 | −0.211749 | ||||||||
\(445\) | −7.05864 | −0.334611 | ||||||||
\(446\) | 19.3445 | 0.915989 | ||||||||
\(447\) | 17.9543 | 0.849211 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 33.3480 | 1.57379 | 0.786894 | − | 0.617088i | \(-0.211688\pi\) | ||||
0.786894 | + | 0.617088i | \(0.211688\pi\) | |||||||
\(450\) | 1.73890 | 0.0819725 | ||||||||
\(451\) | 13.7996 | 0.649800 | ||||||||
\(452\) | −1.94348 | −0.0914137 | ||||||||
\(453\) | 5.67926 | 0.266835 | ||||||||
\(454\) | 9.78761 | 0.459355 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0178327 | 0.000835093 0 | ||||||||
\(457\) | 3.23421 | 0.151290 | 0.0756451 | − | 0.997135i | \(-0.475898\pi\) | ||||
0.0756451 | + | 0.997135i | \(0.475898\pi\) | |||||||
\(458\) | −7.53482 | −0.352079 | ||||||||
\(459\) | −3.39467 | −0.158450 | ||||||||
\(460\) | 18.4068 | 0.858223 | ||||||||
\(461\) | −11.6384 | −0.542052 | −0.271026 | − | 0.962572i | \(-0.587363\pi\) | ||||
−0.271026 | + | 0.962572i | \(0.587363\pi\) | |||||||
\(462\) | −5.12317 | −0.238351 | ||||||||
\(463\) | −13.4682 | −0.625922 | −0.312961 | − | 0.949766i | \(-0.601321\pi\) | ||||
−0.312961 | + | 0.949766i | \(0.601321\pi\) | |||||||
\(464\) | 4.27806 | 0.198604 | ||||||||
\(465\) | −1.11865 | −0.0518760 | ||||||||
\(466\) | 29.4092 | 1.36235 | ||||||||
\(467\) | 40.6722 | 1.88209 | 0.941043 | − | 0.338287i | \(-0.109848\pi\) | ||||
0.941043 | + | 0.338287i | \(0.109848\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.37917 | 0.0636842 | ||||||||
\(470\) | −14.4593 | −0.666957 | ||||||||
\(471\) | 9.36185 | 0.431372 | ||||||||
\(472\) | −13.2304 | −0.608977 | ||||||||
\(473\) | 57.2888 | 2.63414 | ||||||||
\(474\) | 7.29899 | 0.335254 | ||||||||
\(475\) | 0.0310093 | 0.00142280 | ||||||||
\(476\) | 3.39467 | 0.155594 | ||||||||
\(477\) | −9.44524 | −0.432468 | ||||||||
\(478\) | −26.1127 | −1.19437 | ||||||||
\(479\) | −23.0790 | −1.05451 | −0.527253 | − | 0.849709i | \(-0.676778\pi\) | ||||
−0.527253 | + | 0.849709i | \(0.676778\pi\) | |||||||
\(480\) | 2.59594 | 0.118488 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.71173 | −0.0779672 | ||||||||
\(483\) | −7.09063 | −0.322635 | ||||||||
\(484\) | 15.2469 | 0.693039 | ||||||||
\(485\) | 43.4098 | 1.97114 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 32.9859 | 1.49473 | 0.747366 | − | 0.664412i | \(-0.231318\pi\) | ||||
0.747366 | + | 0.664412i | \(0.231318\pi\) | |||||||
\(488\) | −7.25936 | −0.328616 | ||||||||
\(489\) | −15.9019 | −0.719109 | ||||||||
\(490\) | 2.59594 | 0.117273 | ||||||||
\(491\) | −36.9140 | −1.66591 | −0.832953 | − | 0.553343i | \(-0.813352\pi\) | ||||
−0.832953 | + | 0.553343i | \(0.813352\pi\) | |||||||
\(492\) | 2.69358 | 0.121436 | ||||||||
\(493\) | −14.5226 | −0.654066 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.2994 | 0.597765 | ||||||||
\(496\) | −0.430922 | −0.0193490 | ||||||||
\(497\) | −12.7469 | −0.571777 | ||||||||
\(498\) | 2.41028 | 0.108007 | ||||||||
\(499\) | −23.2574 | −1.04114 | −0.520571 | − | 0.853818i | \(-0.674281\pi\) | ||||
−0.520571 | + | 0.853818i | \(0.674281\pi\) | |||||||
\(500\) | −8.46562 | −0.378594 | ||||||||
\(501\) | 22.9624 | 1.02588 | ||||||||
\(502\) | −16.7525 | −0.747702 | ||||||||
\(503\) | 5.83997 | 0.260392 | 0.130196 | − | 0.991488i | \(-0.458439\pi\) | ||||
0.130196 | + | 0.991488i | \(0.458439\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −35.6133 | −1.58477 | ||||||||
\(506\) | 36.3265 | 1.61491 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.1063 | −0.448394 | ||||||||
\(509\) | −24.0780 | −1.06724 | −0.533620 | − | 0.845724i | \(-0.679169\pi\) | ||||
−0.533620 | + | 0.845724i | \(0.679169\pi\) | |||||||
\(510\) | −8.81236 | −0.390218 | ||||||||
\(511\) | 3.14421 | 0.139092 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.0178327 | 0.000787333 0 | ||||||||
\(514\) | −14.6283 | −0.645227 | ||||||||
\(515\) | 11.0300 | 0.486041 | ||||||||
\(516\) | 11.1823 | 0.492274 | ||||||||
\(517\) | −28.5359 | −1.25501 | ||||||||
\(518\) | 4.46183 | 0.196041 | ||||||||
\(519\) | −13.2994 | −0.583780 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.751277 | −0.0329140 | −0.0164570 | − | 0.999865i | \(-0.505239\pi\) | ||||
−0.0164570 | + | 0.999865i | \(0.505239\pi\) | |||||||
\(522\) | 4.27806 | 0.187246 | ||||||||
\(523\) | −37.7779 | −1.65191 | −0.825956 | − | 0.563734i | \(-0.809364\pi\) | ||||
−0.825956 | + | 0.563734i | \(0.809364\pi\) | |||||||
\(524\) | −16.1622 | −0.706049 | ||||||||
\(525\) | −1.73890 | −0.0758918 | ||||||||
\(526\) | 17.3602 | 0.756939 | ||||||||
\(527\) | 1.46284 | 0.0637222 | ||||||||
\(528\) | 5.12317 | 0.222957 | ||||||||
\(529\) | 27.2770 | 1.18596 | ||||||||
\(530\) | −24.5193 | −1.06505 | ||||||||
\(531\) | −13.2304 | −0.574149 | ||||||||
\(532\) | −0.0178327 | −0.000773146 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2.71911 | −0.117667 | ||||||||
\(535\) | −6.30990 | −0.272801 | ||||||||
\(536\) | −1.37917 | −0.0595712 | ||||||||
\(537\) | 11.1476 | 0.481056 | ||||||||
\(538\) | −7.43931 | −0.320732 | ||||||||
\(539\) | 5.12317 | 0.220670 | ||||||||
\(540\) | 2.59594 | 0.111711 | ||||||||
\(541\) | −16.6143 | −0.714304 | −0.357152 | − | 0.934046i | \(-0.616252\pi\) | ||||
−0.357152 | + | 0.934046i | \(0.616252\pi\) | |||||||
\(542\) | 11.3773 | 0.488695 | ||||||||
\(543\) | −18.9951 | −0.815158 | ||||||||
\(544\) | −3.39467 | −0.145545 | ||||||||
\(545\) | 28.0757 | 1.20263 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.7682 | −0.503170 | −0.251585 | − | 0.967835i | \(-0.580952\pi\) | ||||
−0.251585 | + | 0.967835i | \(0.580952\pi\) | |||||||
\(548\) | 11.6110 | 0.495997 | ||||||||
\(549\) | −7.25936 | −0.309822 | ||||||||
\(550\) | 8.90868 | 0.379867 | ||||||||
\(551\) | 0.0762895 | 0.00325004 | ||||||||
\(552\) | 7.09063 | 0.301797 | ||||||||
\(553\) | −7.29899 | −0.310385 | ||||||||
\(554\) | −7.53314 | −0.320052 | ||||||||
\(555\) | −11.5826 | −0.491655 | ||||||||
\(556\) | −9.39315 | −0.398358 | ||||||||
\(557\) | 0.132670 | 0.00562139 | 0.00281070 | − | 0.999996i | \(-0.499105\pi\) | ||||
0.00281070 | + | 0.999996i | \(0.499105\pi\) | |||||||
\(558\) | −0.430922 | −0.0182424 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.59594 | −0.109698 | ||||||||
\(561\) | −17.3915 | −0.734268 | ||||||||
\(562\) | −7.32324 | −0.308912 | ||||||||
\(563\) | 18.1753 | 0.765998 | 0.382999 | − | 0.923749i | \(-0.374891\pi\) | ||||
0.382999 | + | 0.923749i | \(0.374891\pi\) | |||||||
\(564\) | −5.56996 | −0.234538 | ||||||||
\(565\) | −5.04516 | −0.212251 | ||||||||
\(566\) | −12.5399 | −0.527090 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 12.7469 | 0.534849 | ||||||||
\(569\) | 35.8748 | 1.50395 | 0.751974 | − | 0.659193i | \(-0.229102\pi\) | ||||
0.751974 | + | 0.659193i | \(0.229102\pi\) | |||||||
\(570\) | 0.0462926 | 0.00193899 | ||||||||
\(571\) | −38.4148 | −1.60761 | −0.803805 | − | 0.594893i | \(-0.797195\pi\) | ||||
−0.803805 | + | 0.594893i | \(0.797195\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.1986 | −1.01091 | ||||||||
\(574\) | −2.69358 | −0.112428 | ||||||||
\(575\) | 12.3299 | 0.514192 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 35.5854 | 1.48144 | 0.740719 | − | 0.671815i | \(-0.234485\pi\) | ||||
0.740719 | + | 0.671815i | \(0.234485\pi\) | |||||||
\(578\) | −5.47621 | −0.227780 | ||||||||
\(579\) | −10.8065 | −0.449104 | ||||||||
\(580\) | 11.1056 | 0.461135 | ||||||||
\(581\) | −2.41028 | −0.0999954 | ||||||||
\(582\) | 16.7222 | 0.693158 | ||||||||
\(583\) | −48.3896 | −2.00409 | ||||||||
\(584\) | −3.14421 | −0.130108 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.0614 | 0.787421 | ||||||||
\(587\) | 15.3272 | 0.632620 | 0.316310 | − | 0.948656i | \(-0.397556\pi\) | ||||
0.316310 | + | 0.948656i | \(0.397556\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −0.00768450 | −0.000316634 0 | ||||||||
\(590\) | −34.3452 | −1.41397 | ||||||||
\(591\) | −2.43849 | −0.100306 | ||||||||
\(592\) | −4.46183 | −0.183380 | ||||||||
\(593\) | −10.4121 | −0.427574 | −0.213787 | − | 0.976880i | \(-0.568580\pi\) | ||||
−0.213787 | + | 0.976880i | \(0.568580\pi\) | |||||||
\(594\) | 5.12317 | 0.210206 | ||||||||
\(595\) | 8.81236 | 0.361271 | ||||||||
\(596\) | 17.9543 | 0.735438 | ||||||||
\(597\) | 18.5328 | 0.758497 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.4439 | −1.65249 | −0.826246 | − | 0.563309i | \(-0.809528\pi\) | ||||
−0.826246 | + | 0.563309i | \(0.809528\pi\) | |||||||
\(600\) | 1.73890 | 0.0709903 | ||||||||
\(601\) | −12.5291 | −0.511074 | −0.255537 | − | 0.966799i | \(-0.582252\pi\) | ||||
−0.255537 | + | 0.966799i | \(0.582252\pi\) | |||||||
\(602\) | −11.1823 | −0.455757 | ||||||||
\(603\) | −1.37917 | −0.0561642 | ||||||||
\(604\) | 5.67926 | 0.231086 | ||||||||
\(605\) | 39.5799 | 1.60915 | ||||||||
\(606\) | −13.7189 | −0.557290 | ||||||||
\(607\) | −23.0164 | −0.934208 | −0.467104 | − | 0.884202i | \(-0.654703\pi\) | ||||
−0.467104 | + | 0.884202i | \(0.654703\pi\) | |||||||
\(608\) | 0.0178327 | 0.000723212 0 | ||||||||
\(609\) | −4.27806 | −0.173356 | ||||||||
\(610\) | −18.8449 | −0.763006 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.39467 | −0.137221 | ||||||||
\(613\) | −17.2101 | −0.695111 | −0.347556 | − | 0.937659i | \(-0.612988\pi\) | ||||
−0.347556 | + | 0.937659i | \(0.612988\pi\) | |||||||
\(614\) | −24.8387 | −1.00241 | ||||||||
\(615\) | 6.99236 | 0.281959 | ||||||||
\(616\) | −5.12317 | −0.206418 | ||||||||
\(617\) | 5.97264 | 0.240450 | 0.120225 | − | 0.992747i | \(-0.461638\pi\) | ||||
0.120225 | + | 0.992747i | \(0.461638\pi\) | |||||||
\(618\) | 4.24896 | 0.170918 | ||||||||
\(619\) | −22.3969 | −0.900208 | −0.450104 | − | 0.892976i | \(-0.648613\pi\) | ||||
−0.450104 | + | 0.892976i | \(0.648613\pi\) | |||||||
\(620\) | −1.11865 | −0.0449259 | ||||||||
\(621\) | 7.09063 | 0.284537 | ||||||||
\(622\) | −0.438633 | −0.0175876 | ||||||||
\(623\) | 2.71911 | 0.108939 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6707 | −1.22683 | ||||||||
\(626\) | 16.3187 | 0.652228 | ||||||||
\(627\) | 0.0913600 | 0.00364857 | ||||||||
\(628\) | 9.36185 | 0.373579 | ||||||||
\(629\) | 15.1464 | 0.603928 | ||||||||
\(630\) | −2.59594 | −0.103425 | ||||||||
\(631\) | −49.2753 | −1.96162 | −0.980810 | − | 0.194965i | \(-0.937541\pi\) | ||||
−0.980810 | + | 0.194965i | \(0.937541\pi\) | |||||||
\(632\) | 7.29899 | 0.290338 | ||||||||
\(633\) | −6.21752 | −0.247124 | ||||||||
\(634\) | −33.7161 | −1.33904 | ||||||||
\(635\) | −26.2353 | −1.04112 | ||||||||
\(636\) | −9.44524 | −0.374528 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 21.9172 | 0.867712 | ||||||||
\(639\) | 12.7469 | 0.504260 | ||||||||
\(640\) | 2.59594 | 0.102614 | ||||||||
\(641\) | 34.9735 | 1.38137 | 0.690685 | − | 0.723156i | \(-0.257309\pi\) | ||||
0.690685 | + | 0.723156i | \(0.257309\pi\) | |||||||
\(642\) | −2.43068 | −0.0959313 | ||||||||
\(643\) | −8.57982 | −0.338355 | −0.169178 | − | 0.985586i | \(-0.554111\pi\) | ||||
−0.169178 | + | 0.985586i | \(0.554111\pi\) | |||||||
\(644\) | −7.09063 | −0.279410 | ||||||||
\(645\) | 29.0286 | 1.14300 | ||||||||
\(646\) | −0.0605362 | −0.00238176 | ||||||||
\(647\) | −9.80205 | −0.385358 | −0.192679 | − | 0.981262i | \(-0.561718\pi\) | ||||
−0.192679 | + | 0.981262i | \(0.561718\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −67.7813 | −2.66065 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.430922 | 0.0168892 | ||||||||
\(652\) | −15.9019 | −0.622767 | ||||||||
\(653\) | 2.72436 | 0.106612 | 0.0533062 | − | 0.998578i | \(-0.483024\pi\) | ||||
0.0533062 | + | 0.998578i | \(0.483024\pi\) | |||||||
\(654\) | 10.8152 | 0.422909 | ||||||||
\(655\) | −41.9561 | −1.63936 | ||||||||
\(656\) | 2.69358 | 0.105166 | ||||||||
\(657\) | −3.14421 | −0.122667 | ||||||||
\(658\) | 5.56996 | 0.217140 | ||||||||
\(659\) | −16.7458 | −0.652322 | −0.326161 | − | 0.945314i | \(-0.605755\pi\) | ||||
−0.326161 | + | 0.945314i | \(0.605755\pi\) | |||||||
\(660\) | 13.2994 | 0.517680 | ||||||||
\(661\) | 0.629186 | 0.0244725 | 0.0122362 | − | 0.999925i | \(-0.496105\pi\) | ||||
0.0122362 | + | 0.999925i | \(0.496105\pi\) | |||||||
\(662\) | 10.8454 | 0.421520 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.41028 | 0.0935371 | ||||||||
\(665\) | −0.0462926 | −0.00179515 | ||||||||
\(666\) | −4.46183 | −0.172892 | ||||||||
\(667\) | 30.3342 | 1.17454 | ||||||||
\(668\) | 22.9624 | 0.888441 | ||||||||
\(669\) | 19.3445 | 0.747902 | ||||||||
\(670\) | −3.58025 | −0.138317 | ||||||||
\(671\) | −37.1909 | −1.43574 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 14.2637 | 0.549823 | 0.274912 | − | 0.961469i | \(-0.411351\pi\) | ||||
0.274912 | + | 0.961469i | \(0.411351\pi\) | |||||||
\(674\) | −8.64433 | −0.332967 | ||||||||
\(675\) | 1.73890 | 0.0669303 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.8956 | 1.14898 | 0.574491 | − | 0.818511i | \(-0.305200\pi\) | ||||
0.574491 | + | 0.818511i | \(0.305200\pi\) | |||||||
\(678\) | −1.94348 | −0.0746390 | ||||||||
\(679\) | −16.7222 | −0.641739 | ||||||||
\(680\) | −8.81236 | −0.337938 | ||||||||
\(681\) | 9.78761 | 0.375062 | ||||||||
\(682\) | −2.20768 | −0.0845366 | ||||||||
\(683\) | −39.7702 | −1.52176 | −0.760881 | − | 0.648891i | \(-0.775233\pi\) | ||||
−0.760881 | + | 0.648891i | \(0.775233\pi\) | |||||||
\(684\) | 0.0178327 | 0.000681851 0 | ||||||||
\(685\) | 30.1414 | 1.15164 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −7.53482 | −0.287471 | ||||||||
\(688\) | 11.1823 | 0.426321 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.4068 | 0.700736 | ||||||||
\(691\) | −19.1792 | −0.729611 | −0.364806 | − | 0.931084i | \(-0.618865\pi\) | ||||
−0.364806 | + | 0.931084i | \(0.618865\pi\) | |||||||
\(692\) | −13.2994 | −0.505568 | ||||||||
\(693\) | −5.12317 | −0.194613 | ||||||||
\(694\) | −24.0533 | −0.913050 | ||||||||
\(695\) | −24.3840 | −0.924939 | ||||||||
\(696\) | 4.27806 | 0.162160 | ||||||||
\(697\) | −9.14380 | −0.346346 | ||||||||
\(698\) | 31.3486 | 1.18656 | ||||||||
\(699\) | 29.4092 | 1.11236 | ||||||||
\(700\) | −1.73890 | −0.0657242 | ||||||||
\(701\) | 5.24465 | 0.198088 | 0.0990439 | − | 0.995083i | \(-0.468422\pi\) | ||||
0.0990439 | + | 0.995083i | \(0.468422\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0795665 | −0.00300091 | ||||||||
\(704\) | 5.12317 | 0.193087 | ||||||||
\(705\) | −14.4593 | −0.544568 | ||||||||
\(706\) | 11.8086 | 0.444422 | ||||||||
\(707\) | 13.7189 | 0.515950 | ||||||||
\(708\) | −13.2304 | −0.497227 | ||||||||
\(709\) | −30.2825 | −1.13728 | −0.568642 | − | 0.822585i | \(-0.692531\pi\) | ||||
−0.568642 | + | 0.822585i | \(0.692531\pi\) | |||||||
\(710\) | 33.0902 | 1.24185 | ||||||||
\(711\) | 7.29899 | 0.273734 | ||||||||
\(712\) | −2.71911 | −0.101903 | ||||||||
\(713\) | −3.05551 | −0.114430 | ||||||||
\(714\) | 3.39467 | 0.127042 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.1476 | 0.416607 | ||||||||
\(717\) | −26.1127 | −0.975198 | ||||||||
\(718\) | 10.2791 | 0.383612 | ||||||||
\(719\) | −39.3354 | −1.46696 | −0.733481 | − | 0.679710i | \(-0.762106\pi\) | ||||
−0.733481 | + | 0.679710i | \(0.762106\pi\) | |||||||
\(720\) | 2.59594 | 0.0967449 | ||||||||
\(721\) | −4.24896 | −0.158239 | ||||||||
\(722\) | −18.9997 | −0.707095 | ||||||||
\(723\) | −1.71173 | −0.0636600 | ||||||||
\(724\) | −18.9951 | −0.705947 | ||||||||
\(725\) | 7.43913 | 0.276282 | ||||||||
\(726\) | 15.2469 | 0.565864 | ||||||||
\(727\) | 38.5454 | 1.42957 | 0.714785 | − | 0.699344i | \(-0.246525\pi\) | ||||
0.714785 | + | 0.699344i | \(0.246525\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.16217 | −0.302096 | ||||||||
\(731\) | −37.9602 | −1.40401 | ||||||||
\(732\) | −7.25936 | −0.268314 | ||||||||
\(733\) | −9.12968 | −0.337212 | −0.168606 | − | 0.985684i | \(-0.553927\pi\) | ||||
−0.168606 | + | 0.985684i | \(0.553927\pi\) | |||||||
\(734\) | 23.8024 | 0.878564 | ||||||||
\(735\) | 2.59594 | 0.0957527 | ||||||||
\(736\) | 7.09063 | 0.261364 | ||||||||
\(737\) | −7.06573 | −0.260269 | ||||||||
\(738\) | 2.69358 | 0.0991519 | ||||||||
\(739\) | 27.5735 | 1.01431 | 0.507154 | − | 0.861856i | \(-0.330698\pi\) | ||||
0.507154 | + | 0.861856i | \(0.330698\pi\) | |||||||
\(740\) | −11.5826 | −0.425786 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.44524 | 0.346746 | ||||||||
\(743\) | −12.2119 | −0.448010 | −0.224005 | − | 0.974588i | \(-0.571913\pi\) | ||||
−0.224005 | + | 0.974588i | \(0.571913\pi\) | |||||||
\(744\) | −0.430922 | −0.0157984 | ||||||||
\(745\) | 46.6084 | 1.70760 | ||||||||
\(746\) | 4.82143 | 0.176525 | ||||||||
\(747\) | 2.41028 | 0.0881877 | ||||||||
\(748\) | −17.3915 | −0.635895 | ||||||||
\(749\) | 2.43068 | 0.0888151 | ||||||||
\(750\) | −8.46562 | −0.309121 | ||||||||
\(751\) | −8.52238 | −0.310986 | −0.155493 | − | 0.987837i | \(-0.549697\pi\) | ||||
−0.155493 | + | 0.987837i | \(0.549697\pi\) | |||||||
\(752\) | −5.56996 | −0.203116 | ||||||||
\(753\) | −16.7525 | −0.610496 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.7430 | 0.536553 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 1.64966 | 0.0599578 | 0.0299789 | − | 0.999551i | \(-0.490456\pi\) | ||||
0.0299789 | + | 0.999551i | \(0.490456\pi\) | |||||||
\(758\) | 21.2547 | 0.772007 | ||||||||
\(759\) | 36.3265 | 1.31857 | ||||||||
\(760\) | 0.0462926 | 0.00167921 | ||||||||
\(761\) | 29.4180 | 1.06640 | 0.533200 | − | 0.845989i | \(-0.320989\pi\) | ||||
0.533200 | + | 0.845989i | \(0.320989\pi\) | |||||||
\(762\) | −10.1063 | −0.366112 | ||||||||
\(763\) | −10.8152 | −0.391538 | ||||||||
\(764\) | −24.1986 | −0.875475 | ||||||||
\(765\) | −8.81236 | −0.318611 | ||||||||
\(766\) | −32.6499 | −1.17969 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 10.4753 | 0.377750 | 0.188875 | − | 0.982001i | \(-0.439516\pi\) | ||||
0.188875 | + | 0.982001i | \(0.439516\pi\) | |||||||
\(770\) | −13.2994 | −0.479278 | ||||||||
\(771\) | −14.6283 | −0.526826 | ||||||||
\(772\) | −10.8065 | −0.388936 | ||||||||
\(773\) | 44.1861 | 1.58926 | 0.794632 | − | 0.607091i | \(-0.207664\pi\) | ||||
0.794632 | + | 0.607091i | \(0.207664\pi\) | |||||||
\(774\) | 11.1823 | 0.401940 | ||||||||
\(775\) | −0.749330 | −0.0269167 | ||||||||
\(776\) | 16.7222 | 0.600292 | ||||||||
\(777\) | 4.46183 | 0.160067 | ||||||||
\(778\) | −14.8469 | −0.532288 | ||||||||
\(779\) | 0.0480338 | 0.00172099 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 65.3046 | 2.33678 | ||||||||
\(782\) | −24.0703 | −0.860754 | ||||||||
\(783\) | 4.27806 | 0.152886 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 24.3028 | 0.867404 | ||||||||
\(786\) | −16.1622 | −0.576486 | ||||||||
\(787\) | 28.2894 | 1.00841 | 0.504203 | − | 0.863585i | \(-0.331786\pi\) | ||||
0.504203 | + | 0.863585i | \(0.331786\pi\) | |||||||
\(788\) | −2.43849 | −0.0868677 | ||||||||
\(789\) | 17.3602 | 0.618038 | ||||||||
\(790\) | 18.9477 | 0.674130 | ||||||||
\(791\) | 1.94348 | 0.0691023 | ||||||||
\(792\) | 5.12317 | 0.182044 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 15.5132 | 0.550542 | ||||||||
\(795\) | −24.5193 | −0.869609 | ||||||||
\(796\) | 18.5328 | 0.656877 | ||||||||
\(797\) | −30.6493 | −1.08566 | −0.542828 | − | 0.839844i | \(-0.682646\pi\) | ||||
−0.542828 | + | 0.839844i | \(0.682646\pi\) | |||||||
\(798\) | −0.0178327 | −0.000631271 0 | ||||||||
\(799\) | 18.9082 | 0.668924 | ||||||||
\(800\) | 1.73890 | 0.0614794 | ||||||||
\(801\) | −2.71911 | −0.0960749 | ||||||||
\(802\) | 11.1698 | 0.394419 | ||||||||
\(803\) | −16.1083 | −0.568450 | ||||||||
\(804\) | −1.37917 | −0.0486396 | ||||||||
\(805\) | −18.4068 | −0.648756 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.43931 | −0.261876 | ||||||||
\(808\) | −13.7189 | −0.482627 | ||||||||
\(809\) | 28.3202 | 0.995685 | 0.497843 | − | 0.867267i | \(-0.334126\pi\) | ||||
0.497843 | + | 0.867267i | \(0.334126\pi\) | |||||||
\(810\) | 2.59594 | 0.0912120 | ||||||||
\(811\) | 17.1631 | 0.602677 | 0.301338 | − | 0.953517i | \(-0.402567\pi\) | ||||
0.301338 | + | 0.953517i | \(0.402567\pi\) | |||||||
\(812\) | −4.27806 | −0.150131 | ||||||||
\(813\) | 11.3773 | 0.399018 | ||||||||
\(814\) | −22.8587 | −0.801196 | ||||||||
\(815\) | −41.2804 | −1.44599 | ||||||||
\(816\) | −3.39467 | −0.118837 | ||||||||
\(817\) | 0.199411 | 0.00697650 | ||||||||
\(818\) | −1.82157 | −0.0636898 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.99236 | 0.244184 | ||||||||
\(821\) | 31.4722 | 1.09839 | 0.549193 | − | 0.835695i | \(-0.314935\pi\) | ||||
0.549193 | + | 0.835695i | \(0.314935\pi\) | |||||||
\(822\) | 11.6110 | 0.404980 | ||||||||
\(823\) | 6.86696 | 0.239367 | 0.119684 | − | 0.992812i | \(-0.461812\pi\) | ||||
0.119684 | + | 0.992812i | \(0.461812\pi\) | |||||||
\(824\) | 4.24896 | 0.148019 | ||||||||
\(825\) | 8.90868 | 0.310160 | ||||||||
\(826\) | 13.2304 | 0.460343 | ||||||||
\(827\) | 50.9538 | 1.77184 | 0.885918 | − | 0.463842i | \(-0.153529\pi\) | ||||
0.885918 | + | 0.463842i | \(0.153529\pi\) | |||||||
\(828\) | 7.09063 | 0.246416 | ||||||||
\(829\) | −48.0421 | −1.66857 | −0.834285 | − | 0.551333i | \(-0.814119\pi\) | ||||
−0.834285 | + | 0.551333i | \(0.814119\pi\) | |||||||
\(830\) | 6.25695 | 0.217182 | ||||||||
\(831\) | −7.53314 | −0.261322 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.39467 | −0.117618 | ||||||||
\(834\) | −9.39315 | −0.325258 | ||||||||
\(835\) | 59.6089 | 2.06285 | ||||||||
\(836\) | 0.0913600 | 0.00315975 | ||||||||
\(837\) | −0.430922 | −0.0148948 | ||||||||
\(838\) | 30.1385 | 1.04112 | ||||||||
\(839\) | 34.6500 | 1.19625 | 0.598126 | − | 0.801402i | \(-0.295912\pi\) | ||||
0.598126 | + | 0.801402i | \(0.295912\pi\) | |||||||
\(840\) | −2.59594 | −0.0895684 | ||||||||
\(841\) | −10.6982 | −0.368902 | ||||||||
\(842\) | 17.7000 | 0.609982 | ||||||||
\(843\) | −7.32324 | −0.252226 | ||||||||
\(844\) | −6.21752 | −0.214016 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.56996 | −0.191499 | ||||||||
\(847\) | −15.2469 | −0.523888 | ||||||||
\(848\) | −9.44524 | −0.324351 | ||||||||
\(849\) | −12.5399 | −0.430368 | ||||||||
\(850\) | −5.90299 | −0.202471 | ||||||||
\(851\) | −31.6372 | −1.08451 | ||||||||
\(852\) | 12.7469 | 0.436702 | ||||||||
\(853\) | 15.1124 | 0.517439 | 0.258719 | − | 0.965953i | \(-0.416700\pi\) | ||||
0.258719 | + | 0.965953i | \(0.416700\pi\) | |||||||
\(854\) | 7.25936 | 0.248410 | ||||||||
\(855\) | 0.0462926 | 0.00158317 | ||||||||
\(856\) | −2.43068 | −0.0830789 | ||||||||
\(857\) | −30.9270 | −1.05645 | −0.528223 | − | 0.849106i | \(-0.677142\pi\) | ||||
−0.528223 | + | 0.849106i | \(0.677142\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.7434 | −1.59486 | −0.797432 | − | 0.603408i | \(-0.793809\pi\) | ||||
−0.797432 | + | 0.603408i | \(0.793809\pi\) | |||||||
\(860\) | 29.0286 | 0.989867 | ||||||||
\(861\) | −2.69358 | −0.0917968 | ||||||||
\(862\) | −27.9368 | −0.951530 | ||||||||
\(863\) | 26.8891 | 0.915316 | 0.457658 | − | 0.889128i | \(-0.348688\pi\) | ||||
0.457658 | + | 0.889128i | \(0.348688\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −34.5245 | −1.17387 | ||||||||
\(866\) | −26.1856 | −0.889823 | ||||||||
\(867\) | −5.47621 | −0.185982 | ||||||||
\(868\) | 0.430922 | 0.0146264 | ||||||||
\(869\) | 37.3940 | 1.26850 | ||||||||
\(870\) | 11.1056 | 0.376515 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.8152 | 0.366250 | ||||||||
\(873\) | 16.7222 | 0.565961 | ||||||||
\(874\) | 0.126445 | 0.00427707 | ||||||||
\(875\) | 8.46562 | 0.286190 | ||||||||
\(876\) | −3.14421 | −0.106233 | ||||||||
\(877\) | 28.1048 | 0.949033 | 0.474516 | − | 0.880247i | \(-0.342623\pi\) | ||||
0.474516 | + | 0.880247i | \(0.342623\pi\) | |||||||
\(878\) | 7.29808 | 0.246298 | ||||||||
\(879\) | 19.0614 | 0.642927 | ||||||||
\(880\) | 13.2994 | 0.448324 | ||||||||
\(881\) | 21.5473 | 0.725946 | 0.362973 | − | 0.931800i | \(-0.381762\pi\) | ||||
0.362973 | + | 0.931800i | \(0.381762\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −26.4721 | −0.890857 | −0.445429 | − | 0.895317i | \(-0.646949\pi\) | ||||
−0.445429 | + | 0.895317i | \(0.646949\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34.3452 | −1.15450 | ||||||||
\(886\) | −12.0853 | −0.406014 | ||||||||
\(887\) | −1.08719 | −0.0365044 | −0.0182522 | − | 0.999833i | \(-0.505810\pi\) | ||||
−0.0182522 | + | 0.999833i | \(0.505810\pi\) | |||||||
\(888\) | −4.46183 | −0.149729 | ||||||||
\(889\) | 10.1063 | 0.338954 | ||||||||
\(890\) | −7.05864 | −0.236606 | ||||||||
\(891\) | 5.12317 | 0.171633 | ||||||||
\(892\) | 19.3445 | 0.647702 | ||||||||
\(893\) | −0.0993275 | −0.00332387 | ||||||||
\(894\) | 17.9543 | 0.600483 | ||||||||
\(895\) | 28.9386 | 0.967310 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33.3480 | 1.11284 | ||||||||
\(899\) | −1.84351 | −0.0614845 | ||||||||
\(900\) | 1.73890 | 0.0579633 | ||||||||
\(901\) | 32.0635 | 1.06819 | ||||||||
\(902\) | 13.7996 | 0.459478 | ||||||||
\(903\) | −11.1823 | −0.372124 | ||||||||
\(904\) | −1.94348 | −0.0646392 | ||||||||
\(905\) | −49.3101 | −1.63912 | ||||||||
\(906\) | 5.67926 | 0.188681 | ||||||||
\(907\) | 10.3468 | 0.343559 | 0.171780 | − | 0.985135i | \(-0.445048\pi\) | ||||
0.171780 | + | 0.985135i | \(0.445048\pi\) | |||||||
\(908\) | 9.78761 | 0.324813 | ||||||||
\(909\) | −13.7189 | −0.455026 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.7272 | 1.15056 | 0.575281 | − | 0.817956i | \(-0.304893\pi\) | ||||
0.575281 | + | 0.817956i | \(0.304893\pi\) | |||||||
\(912\) | 0.0178327 | 0.000590500 0 | ||||||||
\(913\) | 12.3483 | 0.408669 | ||||||||
\(914\) | 3.23421 | 0.106978 | ||||||||
\(915\) | −18.8449 | −0.622992 | ||||||||
\(916\) | −7.53482 | −0.248957 | ||||||||
\(917\) | 16.1622 | 0.533723 | ||||||||
\(918\) | −3.39467 | −0.112041 | ||||||||
\(919\) | 54.3260 | 1.79205 | 0.896024 | − | 0.444005i | \(-0.146443\pi\) | ||||
0.896024 | + | 0.444005i | \(0.146443\pi\) | |||||||
\(920\) | 18.4068 | 0.606856 | ||||||||
\(921\) | −24.8387 | −0.818462 | ||||||||
\(922\) | −11.6384 | −0.383289 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −5.12317 | −0.168540 | ||||||||
\(925\) | −7.75867 | −0.255103 | ||||||||
\(926\) | −13.4682 | −0.442594 | ||||||||
\(927\) | 4.24896 | 0.139554 | ||||||||
\(928\) | 4.27806 | 0.140434 | ||||||||
\(929\) | −53.7208 | −1.76252 | −0.881261 | − | 0.472630i | \(-0.843305\pi\) | ||||
−0.881261 | + | 0.472630i | \(0.843305\pi\) | |||||||
\(930\) | −1.11865 | −0.0366819 | ||||||||
\(931\) | 0.0178327 | 0.000584444 0 | ||||||||
\(932\) | 29.4092 | 0.963329 | ||||||||
\(933\) | −0.438633 | −0.0143602 | ||||||||
\(934\) | 40.6722 | 1.33084 | ||||||||
\(935\) | −45.1472 | −1.47647 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.4398 | −1.77847 | −0.889236 | − | 0.457449i | \(-0.848763\pi\) | ||||
−0.889236 | + | 0.457449i | \(0.848763\pi\) | |||||||
\(938\) | 1.37917 | 0.0450316 | ||||||||
\(939\) | 16.3187 | 0.532542 | ||||||||
\(940\) | −14.4593 | −0.471610 | ||||||||
\(941\) | 46.9055 | 1.52908 | 0.764538 | − | 0.644578i | \(-0.222967\pi\) | ||||
0.764538 | + | 0.644578i | \(0.222967\pi\) | |||||||
\(942\) | 9.36185 | 0.305026 | ||||||||
\(943\) | 19.0991 | 0.621954 | ||||||||
\(944\) | −13.2304 | −0.430611 | ||||||||
\(945\) | −2.59594 | −0.0844459 | ||||||||
\(946\) | 57.2888 | 1.86262 | ||||||||
\(947\) | −26.2982 | −0.854577 | −0.427288 | − | 0.904115i | \(-0.640531\pi\) | ||||
−0.427288 | + | 0.904115i | \(0.640531\pi\) | |||||||
\(948\) | 7.29899 | 0.237060 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.0310093 | 0.00100607 | ||||||||
\(951\) | −33.7161 | −1.09332 | ||||||||
\(952\) | 3.39467 | 0.110022 | ||||||||
\(953\) | −31.6256 | −1.02445 | −0.512227 | − | 0.858850i | \(-0.671179\pi\) | ||||
−0.512227 | + | 0.858850i | \(0.671179\pi\) | |||||||
\(954\) | −9.44524 | −0.305801 | ||||||||
\(955\) | −62.8181 | −2.03275 | ||||||||
\(956\) | −26.1127 | −0.844546 | ||||||||
\(957\) | 21.9172 | 0.708484 | ||||||||
\(958\) | −23.0790 | −0.745648 | ||||||||
\(959\) | −11.6110 | −0.374938 | ||||||||
\(960\) | 2.59594 | 0.0837836 | ||||||||
\(961\) | −30.8143 | −0.994010 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.43068 | −0.0783276 | ||||||||
\(964\) | −1.71173 | −0.0551312 | ||||||||
\(965\) | −28.0531 | −0.903061 | ||||||||
\(966\) | −7.09063 | −0.228137 | ||||||||
\(967\) | −13.0712 | −0.420340 | −0.210170 | − | 0.977665i | \(-0.567402\pi\) | ||||
−0.210170 | + | 0.977665i | \(0.567402\pi\) | |||||||
\(968\) | 15.2469 | 0.490052 | ||||||||
\(969\) | −0.0605362 | −0.00194470 | ||||||||
\(970\) | 43.4098 | 1.39381 | ||||||||
\(971\) | −50.7418 | −1.62838 | −0.814190 | − | 0.580598i | \(-0.802819\pi\) | ||||
−0.814190 | + | 0.580598i | \(0.802819\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 9.39315 | 0.301130 | ||||||||
\(974\) | 32.9859 | 1.05694 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.25936 | −0.232366 | ||||||||
\(977\) | 9.21878 | 0.294935 | 0.147467 | − | 0.989067i | \(-0.452888\pi\) | ||||
0.147467 | + | 0.989067i | \(0.452888\pi\) | |||||||
\(978\) | −15.9019 | −0.508487 | ||||||||
\(979\) | −13.9304 | −0.445219 | ||||||||
\(980\) | 2.59594 | 0.0829242 | ||||||||
\(981\) | 10.8152 | 0.345304 | ||||||||
\(982\) | −36.9140 | −1.17797 | ||||||||
\(983\) | 4.08873 | 0.130410 | 0.0652052 | − | 0.997872i | \(-0.479230\pi\) | ||||
0.0652052 | + | 0.997872i | \(0.479230\pi\) | |||||||
\(984\) | 2.69358 | 0.0858681 | ||||||||
\(985\) | −6.33018 | −0.201696 | ||||||||
\(986\) | −14.5226 | −0.462494 | ||||||||
\(987\) | 5.56996 | 0.177294 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 79.2896 | 2.52126 | ||||||||
\(990\) | 13.2994 | 0.422684 | ||||||||
\(991\) | −3.90744 | −0.124124 | −0.0620620 | − | 0.998072i | \(-0.519768\pi\) | ||||
−0.0620620 | + | 0.998072i | \(0.519768\pi\) | |||||||
\(992\) | −0.430922 | −0.0136818 | ||||||||
\(993\) | 10.8454 | 0.344170 | ||||||||
\(994\) | −12.7469 | −0.404308 | ||||||||
\(995\) | 48.1100 | 1.52519 | ||||||||
\(996\) | 2.41028 | 0.0763728 | ||||||||
\(997\) | 2.76475 | 0.0875604 | 0.0437802 | − | 0.999041i | \(-0.486060\pi\) | ||||
0.0437802 | + | 0.999041i | \(0.486060\pi\) | |||||||
\(998\) | −23.2574 | −0.736199 | ||||||||
\(999\) | −4.46183 | −0.141166 |
(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 | 7098.2.a.cu.1.4 | yes | 6 | |
13.12 | even | 2 | 7098.2.a.cq.1.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cq.1.3 | ✓ | 6 | 13.12 | even | 2 | ||
7098.2.a.cu.1.4 | yes | 6 | 1.1 | even | 1 | trivial |