Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, 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("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 966) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(5\) | −3.70156 | −1.65539 | −0.827694 | − | 0.561179i | \(-0.810348\pi\) | ||||
−0.827694 | + | 0.561179i | \(0.810348\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.70156 | 1.17054 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −5.70156 | −1.58133 | −0.790664 | − | 0.612250i | \(-0.790265\pi\) | ||||
−0.790664 | + | 0.612250i | \(0.790265\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.70156 | 0.955739 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.40312 | 1.23956 | 0.619781 | − | 0.784775i | \(-0.287221\pi\) | ||||
0.619781 | + | 0.784775i | \(0.287221\pi\) | |||||||
\(20\) | −3.70156 | −0.827694 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.852803 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 8.70156 | 1.74031 | ||||||||
\(26\) | 5.70156 | 1.11817 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.298438 | 0.0554185 | 0.0277093 | − | 0.999616i | \(-0.491179\pi\) | ||||
0.0277093 | + | 0.999616i | \(0.491179\pi\) | |||||||
\(30\) | −3.70156 | −0.675810 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.00000 | 0.696311 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.29844 | 0.706659 | 0.353329 | − | 0.935499i | \(-0.385049\pi\) | ||||
0.353329 | + | 0.935499i | \(0.385049\pi\) | |||||||
\(38\) | −5.40312 | −0.876502 | ||||||||
\(39\) | 5.70156 | 0.912981 | ||||||||
\(40\) | 3.70156 | 0.585268 | ||||||||
\(41\) | 0.298438 | 0.0466082 | 0.0233041 | − | 0.999728i | \(-0.492581\pi\) | ||||
0.0233041 | + | 0.999728i | \(0.492581\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.70156 | −0.259486 | −0.129743 | − | 0.991548i | \(-0.541415\pi\) | ||||
−0.129743 | + | 0.991548i | \(0.541415\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | −3.70156 | −0.551796 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 11.1047 | 1.61978 | 0.809892 | − | 0.586578i | \(-0.199525\pi\) | ||||
0.809892 | + | 0.586578i | \(0.199525\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.70156 | −1.23059 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | −5.70156 | −0.790664 | ||||||||
\(53\) | −9.40312 | −1.29162 | −0.645809 | − | 0.763499i | \(-0.723480\pi\) | ||||
−0.645809 | + | 0.763499i | \(0.723480\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 14.8062 | 1.99647 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.40312 | −0.715661 | ||||||||
\(58\) | −0.298438 | −0.0391868 | ||||||||
\(59\) | 7.40312 | 0.963805 | 0.481902 | − | 0.876225i | \(-0.339946\pi\) | ||||
0.481902 | + | 0.876225i | \(0.339946\pi\) | |||||||
\(60\) | 3.70156 | 0.477870 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 21.1047 | 2.61771 | ||||||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | 14.8062 | 1.80887 | 0.904436 | − | 0.426610i | \(-0.140292\pi\) | ||||
0.904436 | + | 0.426610i | \(0.140292\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.40312 | −0.878589 | −0.439295 | − | 0.898343i | \(-0.644772\pi\) | ||||
−0.439295 | + | 0.898343i | \(0.644772\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −1.40312 | −0.164223 | −0.0821116 | − | 0.996623i | \(-0.526166\pi\) | ||||
−0.0821116 | + | 0.996623i | \(0.526166\pi\) | |||||||
\(74\) | −4.29844 | −0.499683 | ||||||||
\(75\) | −8.70156 | −1.00477 | ||||||||
\(76\) | 5.40312 | 0.619781 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.70156 | −0.645575 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −3.70156 | −0.413847 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.298438 | −0.0329570 | ||||||||
\(83\) | −13.4031 | −1.47118 | −0.735592 | − | 0.677425i | \(-0.763096\pi\) | ||||
−0.735592 | + | 0.677425i | \(0.763096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.8062 | 1.60596 | ||||||||
\(86\) | 1.70156 | 0.183484 | ||||||||
\(87\) | −0.298438 | −0.0319959 | ||||||||
\(88\) | 4.00000 | 0.426401 | ||||||||
\(89\) | 11.4031 | 1.20873 | 0.604364 | − | 0.796708i | \(-0.293427\pi\) | ||||
0.604364 | + | 0.796708i | \(0.293427\pi\) | |||||||
\(90\) | 3.70156 | 0.390179 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | −11.1047 | −1.14536 | ||||||||
\(95\) | −20.0000 | −2.05196 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −6.29844 | −0.639509 | −0.319755 | − | 0.947500i | \(-0.603601\pi\) | ||||
−0.319755 | + | 0.947500i | \(0.603601\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 8.70156 | 0.870156 | ||||||||
\(101\) | 3.40312 | 0.338624 | 0.169312 | − | 0.985563i | \(-0.445846\pi\) | ||||
0.169312 | + | 0.985563i | \(0.445846\pi\) | |||||||
\(102\) | −4.00000 | −0.396059 | ||||||||
\(103\) | −2.29844 | −0.226472 | −0.113236 | − | 0.993568i | \(-0.536122\pi\) | ||||
−0.113236 | + | 0.993568i | \(0.536122\pi\) | |||||||
\(104\) | 5.70156 | 0.559084 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.40312 | 0.913312 | ||||||||
\(107\) | 18.8062 | 1.81807 | 0.909034 | − | 0.416721i | \(-0.136821\pi\) | ||||
0.909034 | + | 0.416721i | \(0.136821\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −7.70156 | −0.737676 | −0.368838 | − | 0.929494i | \(-0.620244\pi\) | ||||
−0.368838 | + | 0.929494i | \(0.620244\pi\) | |||||||
\(110\) | −14.8062 | −1.41172 | ||||||||
\(111\) | −4.29844 | −0.407990 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.10469 | 0.668353 | 0.334176 | − | 0.942511i | \(-0.391542\pi\) | ||||
0.334176 | + | 0.942511i | \(0.391542\pi\) | |||||||
\(114\) | 5.40312 | 0.506049 | ||||||||
\(115\) | −3.70156 | −0.345172 | ||||||||
\(116\) | 0.298438 | 0.0277093 | ||||||||
\(117\) | −5.70156 | −0.527110 | ||||||||
\(118\) | −7.40312 | −0.681513 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.70156 | −0.337905 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | −0.298438 | −0.0269092 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | −13.7016 | −1.22550 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.70156 | −0.505932 | −0.252966 | − | 0.967475i | \(-0.581406\pi\) | ||||
−0.252966 | + | 0.967475i | \(0.581406\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.70156 | 0.149814 | ||||||||
\(130\) | −21.1047 | −1.85100 | ||||||||
\(131\) | 7.40312 | 0.646814 | 0.323407 | − | 0.946260i | \(-0.395172\pi\) | ||||
0.323407 | + | 0.946260i | \(0.395172\pi\) | |||||||
\(132\) | 4.00000 | 0.348155 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.8062 | −1.27907 | ||||||||
\(135\) | 3.70156 | 0.318580 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | −19.7016 | −1.68322 | −0.841609 | − | 0.540087i | \(-0.818391\pi\) | ||||
−0.841609 | + | 0.540087i | \(0.818391\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | −17.7016 | −1.50143 | −0.750713 | − | 0.660628i | \(-0.770290\pi\) | ||||
−0.750713 | + | 0.660628i | \(0.770290\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.1047 | −0.935183 | ||||||||
\(142\) | 7.40312 | 0.621256 | ||||||||
\(143\) | 22.8062 | 1.90715 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.10469 | −0.0917392 | ||||||||
\(146\) | 1.40312 | 0.116123 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.29844 | 0.353329 | ||||||||
\(149\) | −20.2094 | −1.65562 | −0.827808 | − | 0.561011i | \(-0.810412\pi\) | ||||
−0.827808 | + | 0.561011i | \(0.810412\pi\) | |||||||
\(150\) | 8.70156 | 0.710480 | ||||||||
\(151\) | 23.9109 | 1.94584 | 0.972922 | − | 0.231133i | \(-0.0742433\pi\) | ||||
0.972922 | + | 0.231133i | \(0.0742433\pi\) | |||||||
\(152\) | −5.40312 | −0.438251 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.40312 | −0.594633 | ||||||||
\(156\) | 5.70156 | 0.456490 | ||||||||
\(157\) | 1.40312 | 0.111982 | 0.0559908 | − | 0.998431i | \(-0.482168\pi\) | ||||
0.0559908 | + | 0.998431i | \(0.482168\pi\) | |||||||
\(158\) | −8.00000 | −0.636446 | ||||||||
\(159\) | 9.40312 | 0.745716 | ||||||||
\(160\) | 3.70156 | 0.292634 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −10.8062 | −0.846411 | −0.423205 | − | 0.906034i | \(-0.639095\pi\) | ||||
−0.423205 | + | 0.906034i | \(0.639095\pi\) | |||||||
\(164\) | 0.298438 | 0.0233041 | ||||||||
\(165\) | −14.8062 | −1.15266 | ||||||||
\(166\) | 13.4031 | 1.04028 | ||||||||
\(167\) | 13.4031 | 1.03716 | 0.518582 | − | 0.855028i | \(-0.326460\pi\) | ||||
0.518582 | + | 0.855028i | \(0.326460\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.5078 | 1.50060 | ||||||||
\(170\) | −14.8062 | −1.13559 | ||||||||
\(171\) | 5.40312 | 0.413187 | ||||||||
\(172\) | −1.70156 | −0.129743 | ||||||||
\(173\) | −19.4031 | −1.47519 | −0.737596 | − | 0.675242i | \(-0.764039\pi\) | ||||
−0.737596 | + | 0.675242i | \(0.764039\pi\) | |||||||
\(174\) | 0.298438 | 0.0226245 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | −7.40312 | −0.556453 | ||||||||
\(178\) | −11.4031 | −0.854700 | ||||||||
\(179\) | −25.1047 | −1.87641 | −0.938206 | − | 0.346077i | \(-0.887514\pi\) | ||||
−0.938206 | + | 0.346077i | \(0.887514\pi\) | |||||||
\(180\) | −3.70156 | −0.275898 | ||||||||
\(181\) | 16.8062 | 1.24920 | 0.624599 | − | 0.780945i | \(-0.285262\pi\) | ||||
0.624599 | + | 0.780945i | \(0.285262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −15.9109 | −1.16980 | ||||||||
\(186\) | 2.00000 | 0.146647 | ||||||||
\(187\) | 16.0000 | 1.17004 | ||||||||
\(188\) | 11.1047 | 0.809892 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 20.0000 | 1.45095 | ||||||||
\(191\) | 22.8062 | 1.65020 | 0.825101 | − | 0.564985i | \(-0.191118\pi\) | ||||
0.825101 | + | 0.564985i | \(0.191118\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −23.1047 | −1.66311 | −0.831556 | − | 0.555441i | \(-0.812549\pi\) | ||||
−0.831556 | + | 0.555441i | \(0.812549\pi\) | |||||||
\(194\) | 6.29844 | 0.452201 | ||||||||
\(195\) | −21.1047 | −1.51134 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.5078 | 1.60362 | 0.801808 | − | 0.597582i | \(-0.203872\pi\) | ||||
0.801808 | + | 0.597582i | \(0.203872\pi\) | |||||||
\(198\) | 4.00000 | 0.284268 | ||||||||
\(199\) | 2.29844 | 0.162932 | 0.0814660 | − | 0.996676i | \(-0.474040\pi\) | ||||
0.0814660 | + | 0.996676i | \(0.474040\pi\) | |||||||
\(200\) | −8.70156 | −0.615293 | ||||||||
\(201\) | −14.8062 | −1.04435 | ||||||||
\(202\) | −3.40312 | −0.239443 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | −1.10469 | −0.0771546 | ||||||||
\(206\) | 2.29844 | 0.160140 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −5.70156 | −0.395332 | ||||||||
\(209\) | −21.6125 | −1.49497 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.8062 | 0.743933 | 0.371966 | − | 0.928246i | \(-0.378684\pi\) | ||||
0.371966 | + | 0.928246i | \(0.378684\pi\) | |||||||
\(212\) | −9.40312 | −0.645809 | ||||||||
\(213\) | 7.40312 | 0.507254 | ||||||||
\(214\) | −18.8062 | −1.28557 | ||||||||
\(215\) | 6.29844 | 0.429550 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.70156 | 0.521616 | ||||||||
\(219\) | 1.40312 | 0.0948143 | ||||||||
\(220\) | 14.8062 | 0.998237 | ||||||||
\(221\) | 22.8062 | 1.53411 | ||||||||
\(222\) | 4.29844 | 0.288492 | ||||||||
\(223\) | 22.0000 | 1.47323 | 0.736614 | − | 0.676313i | \(-0.236423\pi\) | ||||
0.736614 | + | 0.676313i | \(0.236423\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.70156 | 0.580104 | ||||||||
\(226\) | −7.10469 | −0.472597 | ||||||||
\(227\) | 23.1047 | 1.53351 | 0.766756 | − | 0.641939i | \(-0.221870\pi\) | ||||
0.766756 | + | 0.641939i | \(0.221870\pi\) | |||||||
\(228\) | −5.40312 | −0.357831 | ||||||||
\(229\) | 14.5969 | 0.964589 | 0.482294 | − | 0.876009i | \(-0.339804\pi\) | ||||
0.482294 | + | 0.876009i | \(0.339804\pi\) | |||||||
\(230\) | 3.70156 | 0.244074 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.298438 | −0.0195934 | ||||||||
\(233\) | −26.0000 | −1.70332 | −0.851658 | − | 0.524097i | \(-0.824403\pi\) | ||||
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 5.70156 | 0.372723 | ||||||||
\(235\) | −41.1047 | −2.68137 | ||||||||
\(236\) | 7.40312 | 0.481902 | ||||||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.8062 | 0.698998 | 0.349499 | − | 0.936937i | \(-0.386352\pi\) | ||||
0.349499 | + | 0.936937i | \(0.386352\pi\) | |||||||
\(240\) | 3.70156 | 0.238935 | ||||||||
\(241\) | 15.9109 | 1.02491 | 0.512457 | − | 0.858713i | \(-0.328736\pi\) | ||||
0.512457 | + | 0.858713i | \(0.328736\pi\) | |||||||
\(242\) | −5.00000 | −0.321412 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.298438 | 0.0190277 | ||||||||
\(247\) | −30.8062 | −1.96015 | ||||||||
\(248\) | −2.00000 | −0.127000 | ||||||||
\(249\) | 13.4031 | 0.849388 | ||||||||
\(250\) | 13.7016 | 0.866563 | ||||||||
\(251\) | −19.7016 | −1.24355 | −0.621776 | − | 0.783195i | \(-0.713588\pi\) | ||||
−0.621776 | + | 0.783195i | \(0.713588\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 5.70156 | 0.357748 | ||||||||
\(255\) | −14.8062 | −0.927203 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.00000 | −0.124757 | −0.0623783 | − | 0.998053i | \(-0.519869\pi\) | ||||
−0.0623783 | + | 0.998053i | \(0.519869\pi\) | |||||||
\(258\) | −1.70156 | −0.105935 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 21.1047 | 1.30886 | ||||||||
\(261\) | 0.298438 | 0.0184728 | ||||||||
\(262\) | −7.40312 | −0.457367 | ||||||||
\(263\) | 9.70156 | 0.598224 | 0.299112 | − | 0.954218i | \(-0.403310\pi\) | ||||
0.299112 | + | 0.954218i | \(0.403310\pi\) | |||||||
\(264\) | −4.00000 | −0.246183 | ||||||||
\(265\) | 34.8062 | 2.13813 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.4031 | −0.697860 | ||||||||
\(268\) | 14.8062 | 0.904436 | ||||||||
\(269\) | 10.2094 | 0.622476 | 0.311238 | − | 0.950332i | \(-0.399256\pi\) | ||||
0.311238 | + | 0.950332i | \(0.399256\pi\) | |||||||
\(270\) | −3.70156 | −0.225270 | ||||||||
\(271\) | −1.40312 | −0.0852337 | −0.0426169 | − | 0.999091i | \(-0.513569\pi\) | ||||
−0.0426169 | + | 0.999091i | \(0.513569\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.7016 | 1.19021 | ||||||||
\(275\) | −34.8062 | −2.09890 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | −21.4031 | −1.28599 | −0.642995 | − | 0.765871i | \(-0.722308\pi\) | ||||
−0.642995 | + | 0.765871i | \(0.722308\pi\) | |||||||
\(278\) | 17.7016 | 1.06167 | ||||||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5078 | 0.865463 | 0.432732 | − | 0.901523i | \(-0.357550\pi\) | ||||
0.432732 | + | 0.901523i | \(0.357550\pi\) | |||||||
\(282\) | 11.1047 | 0.661274 | ||||||||
\(283\) | −4.80625 | −0.285702 | −0.142851 | − | 0.989744i | \(-0.545627\pi\) | ||||
−0.142851 | + | 0.989744i | \(0.545627\pi\) | |||||||
\(284\) | −7.40312 | −0.439295 | ||||||||
\(285\) | 20.0000 | 1.18470 | ||||||||
\(286\) | −22.8062 | −1.34856 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 1.10469 | 0.0648694 | ||||||||
\(291\) | 6.29844 | 0.369221 | ||||||||
\(292\) | −1.40312 | −0.0821116 | ||||||||
\(293\) | 20.8062 | 1.21551 | 0.607757 | − | 0.794123i | \(-0.292069\pi\) | ||||
0.607757 | + | 0.794123i | \(0.292069\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.4031 | −1.59547 | ||||||||
\(296\) | −4.29844 | −0.249842 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | 20.2094 | 1.17070 | ||||||||
\(299\) | −5.70156 | −0.329730 | ||||||||
\(300\) | −8.70156 | −0.502385 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −23.9109 | −1.37592 | ||||||||
\(303\) | −3.40312 | −0.195504 | ||||||||
\(304\) | 5.40312 | 0.309890 | ||||||||
\(305\) | −7.40312 | −0.423902 | ||||||||
\(306\) | 4.00000 | 0.228665 | ||||||||
\(307\) | −11.9109 | −0.679793 | −0.339896 | − | 0.940463i | \(-0.610392\pi\) | ||||
−0.339896 | + | 0.940463i | \(0.610392\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.29844 | 0.130754 | ||||||||
\(310\) | 7.40312 | 0.420469 | ||||||||
\(311\) | −13.4031 | −0.760021 | −0.380011 | − | 0.924982i | \(-0.624080\pi\) | ||||
−0.380011 | + | 0.924982i | \(0.624080\pi\) | |||||||
\(312\) | −5.70156 | −0.322787 | ||||||||
\(313\) | 6.20937 | 0.350974 | 0.175487 | − | 0.984482i | \(-0.443850\pi\) | ||||
0.175487 | + | 0.984482i | \(0.443850\pi\) | |||||||
\(314\) | −1.40312 | −0.0791829 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | −8.29844 | −0.466087 | −0.233043 | − | 0.972466i | \(-0.574868\pi\) | ||||
−0.233043 | + | 0.972466i | \(0.574868\pi\) | |||||||
\(318\) | −9.40312 | −0.527301 | ||||||||
\(319\) | −1.19375 | −0.0668373 | ||||||||
\(320\) | −3.70156 | −0.206924 | ||||||||
\(321\) | −18.8062 | −1.04966 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.6125 | −1.20255 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −49.6125 | −2.75201 | ||||||||
\(326\) | 10.8062 | 0.598503 | ||||||||
\(327\) | 7.70156 | 0.425897 | ||||||||
\(328\) | −0.298438 | −0.0164785 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 14.8062 | 0.815057 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | −13.4031 | −0.735592 | ||||||||
\(333\) | 4.29844 | 0.235553 | ||||||||
\(334\) | −13.4031 | −0.733386 | ||||||||
\(335\) | −54.8062 | −2.99439 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.20937 | −0.229299 | −0.114650 | − | 0.993406i | \(-0.536575\pi\) | ||||
−0.114650 | + | 0.993406i | \(0.536575\pi\) | |||||||
\(338\) | −19.5078 | −1.06109 | ||||||||
\(339\) | −7.10469 | −0.385874 | ||||||||
\(340\) | 14.8062 | 0.802982 | ||||||||
\(341\) | −8.00000 | −0.433224 | ||||||||
\(342\) | −5.40312 | −0.292167 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.70156 | 0.0917421 | ||||||||
\(345\) | 3.70156 | 0.199285 | ||||||||
\(346\) | 19.4031 | 1.04312 | ||||||||
\(347\) | −10.2984 | −0.552849 | −0.276425 | − | 0.961036i | \(-0.589150\pi\) | ||||
−0.276425 | + | 0.961036i | \(0.589150\pi\) | |||||||
\(348\) | −0.298438 | −0.0159979 | ||||||||
\(349\) | −12.5969 | −0.674295 | −0.337148 | − | 0.941452i | \(-0.609462\pi\) | ||||
−0.337148 | + | 0.941452i | \(0.609462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.70156 | 0.304327 | ||||||||
\(352\) | 4.00000 | 0.213201 | ||||||||
\(353\) | −4.29844 | −0.228783 | −0.114391 | − | 0.993436i | \(-0.536492\pi\) | ||||
−0.114391 | + | 0.993436i | \(0.536492\pi\) | |||||||
\(354\) | 7.40312 | 0.393472 | ||||||||
\(355\) | 27.4031 | 1.45441 | ||||||||
\(356\) | 11.4031 | 0.604364 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.1047 | 1.32682 | ||||||||
\(359\) | −2.89531 | −0.152809 | −0.0764044 | − | 0.997077i | \(-0.524344\pi\) | ||||
−0.0764044 | + | 0.997077i | \(0.524344\pi\) | |||||||
\(360\) | 3.70156 | 0.195089 | ||||||||
\(361\) | 10.1938 | 0.536513 | ||||||||
\(362\) | −16.8062 | −0.883317 | ||||||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.19375 | 0.271853 | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | 17.1047 | 0.892857 | 0.446429 | − | 0.894819i | \(-0.352696\pi\) | ||||
0.446429 | + | 0.894819i | \(0.352696\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0.298438 | 0.0155361 | ||||||||
\(370\) | 15.9109 | 0.827170 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.00000 | −0.103695 | ||||||||
\(373\) | −0.806248 | −0.0417460 | −0.0208730 | − | 0.999782i | \(-0.506645\pi\) | ||||
−0.0208730 | + | 0.999782i | \(0.506645\pi\) | |||||||
\(374\) | −16.0000 | −0.827340 | ||||||||
\(375\) | 13.7016 | 0.707546 | ||||||||
\(376\) | −11.1047 | −0.572680 | ||||||||
\(377\) | −1.70156 | −0.0876349 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.7016 | 0.703802 | 0.351901 | − | 0.936037i | \(-0.385535\pi\) | ||||
0.351901 | + | 0.936037i | \(0.385535\pi\) | |||||||
\(380\) | −20.0000 | −1.02598 | ||||||||
\(381\) | 5.70156 | 0.292100 | ||||||||
\(382\) | −22.8062 | −1.16687 | ||||||||
\(383\) | −29.6125 | −1.51313 | −0.756564 | − | 0.653920i | \(-0.773123\pi\) | ||||
−0.756564 | + | 0.653920i | \(0.773123\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.1047 | 1.17600 | ||||||||
\(387\) | −1.70156 | −0.0864953 | ||||||||
\(388\) | −6.29844 | −0.319755 | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 21.1047 | 1.06868 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.40312 | −0.373438 | ||||||||
\(394\) | −22.5078 | −1.13393 | ||||||||
\(395\) | −29.6125 | −1.48997 | ||||||||
\(396\) | −4.00000 | −0.201008 | ||||||||
\(397\) | −8.59688 | −0.431465 | −0.215732 | − | 0.976453i | \(-0.569214\pi\) | ||||
−0.215732 | + | 0.976453i | \(0.569214\pi\) | |||||||
\(398\) | −2.29844 | −0.115210 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.70156 | 0.435078 | ||||||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 14.8062 | 0.738469 | ||||||||
\(403\) | −11.4031 | −0.568030 | ||||||||
\(404\) | 3.40312 | 0.169312 | ||||||||
\(405\) | −3.70156 | −0.183932 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.1938 | −0.852263 | ||||||||
\(408\) | −4.00000 | −0.198030 | ||||||||
\(409\) | −5.40312 | −0.267167 | −0.133584 | − | 0.991038i | \(-0.542648\pi\) | ||||
−0.133584 | + | 0.991038i | \(0.542648\pi\) | |||||||
\(410\) | 1.10469 | 0.0545566 | ||||||||
\(411\) | 19.7016 | 0.971806 | ||||||||
\(412\) | −2.29844 | −0.113236 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 49.6125 | 2.43538 | ||||||||
\(416\) | 5.70156 | 0.279542 | ||||||||
\(417\) | 17.7016 | 0.866849 | ||||||||
\(418\) | 21.6125 | 1.05710 | ||||||||
\(419\) | 0.209373 | 0.0102285 | 0.00511426 | − | 0.999987i | \(-0.498372\pi\) | ||||
0.00511426 | + | 0.999987i | \(0.498372\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7016 | −0.765247 | −0.382624 | − | 0.923904i | \(-0.624979\pi\) | ||||
−0.382624 | + | 0.923904i | \(0.624979\pi\) | |||||||
\(422\) | −10.8062 | −0.526040 | ||||||||
\(423\) | 11.1047 | 0.539928 | ||||||||
\(424\) | 9.40312 | 0.456656 | ||||||||
\(425\) | −34.8062 | −1.68835 | ||||||||
\(426\) | −7.40312 | −0.358683 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.8062 | 0.909034 | ||||||||
\(429\) | −22.8062 | −1.10110 | ||||||||
\(430\) | −6.29844 | −0.303738 | ||||||||
\(431\) | −3.91093 | −0.188383 | −0.0941916 | − | 0.995554i | \(-0.530027\pi\) | ||||
−0.0941916 | + | 0.995554i | \(0.530027\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −31.3141 | −1.50486 | −0.752429 | − | 0.658674i | \(-0.771118\pi\) | ||||
−0.752429 | + | 0.658674i | \(0.771118\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.10469 | 0.0529657 | ||||||||
\(436\) | −7.70156 | −0.368838 | ||||||||
\(437\) | 5.40312 | 0.258466 | ||||||||
\(438\) | −1.40312 | −0.0670439 | ||||||||
\(439\) | 22.0000 | 1.05000 | 0.525001 | − | 0.851101i | \(-0.324065\pi\) | ||||
0.525001 | + | 0.851101i | \(0.324065\pi\) | |||||||
\(440\) | −14.8062 | −0.705860 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.8062 | −1.08478 | ||||||||
\(443\) | −13.7016 | −0.650981 | −0.325490 | − | 0.945545i | \(-0.605529\pi\) | ||||
−0.325490 | + | 0.945545i | \(0.605529\pi\) | |||||||
\(444\) | −4.29844 | −0.203995 | ||||||||
\(445\) | −42.2094 | −2.00092 | ||||||||
\(446\) | −22.0000 | −1.04173 | ||||||||
\(447\) | 20.2094 | 0.955871 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.4187 | −1.81309 | −0.906546 | − | 0.422106i | \(-0.861291\pi\) | ||||
−0.906546 | + | 0.422106i | \(0.861291\pi\) | |||||||
\(450\) | −8.70156 | −0.410196 | ||||||||
\(451\) | −1.19375 | −0.0562116 | ||||||||
\(452\) | 7.10469 | 0.334176 | ||||||||
\(453\) | −23.9109 | −1.12343 | ||||||||
\(454\) | −23.1047 | −1.08436 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.40312 | 0.253024 | ||||||||
\(457\) | 28.2094 | 1.31958 | 0.659789 | − | 0.751451i | \(-0.270645\pi\) | ||||
0.659789 | + | 0.751451i | \(0.270645\pi\) | |||||||
\(458\) | −14.5969 | −0.682067 | ||||||||
\(459\) | 4.00000 | 0.186704 | ||||||||
\(460\) | −3.70156 | −0.172586 | ||||||||
\(461\) | 2.20937 | 0.102901 | 0.0514504 | − | 0.998676i | \(-0.483616\pi\) | ||||
0.0514504 | + | 0.998676i | \(0.483616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.2984 | −1.03630 | −0.518148 | − | 0.855291i | \(-0.673378\pi\) | ||||
−0.518148 | + | 0.855291i | \(0.673378\pi\) | |||||||
\(464\) | 0.298438 | 0.0138546 | ||||||||
\(465\) | 7.40312 | 0.343312 | ||||||||
\(466\) | 26.0000 | 1.20443 | ||||||||
\(467\) | 3.70156 | 0.171288 | 0.0856439 | − | 0.996326i | \(-0.472705\pi\) | ||||
0.0856439 | + | 0.996326i | \(0.472705\pi\) | |||||||
\(468\) | −5.70156 | −0.263555 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 41.1047 | 1.89602 | ||||||||
\(471\) | −1.40312 | −0.0646526 | ||||||||
\(472\) | −7.40312 | −0.340756 | ||||||||
\(473\) | 6.80625 | 0.312952 | ||||||||
\(474\) | 8.00000 | 0.367452 | ||||||||
\(475\) | 47.0156 | 2.15722 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.40312 | −0.430539 | ||||||||
\(478\) | −10.8062 | −0.494266 | ||||||||
\(479\) | −16.5969 | −0.758331 | −0.379165 | − | 0.925329i | \(-0.623789\pi\) | ||||
−0.379165 | + | 0.925329i | \(0.623789\pi\) | |||||||
\(480\) | −3.70156 | −0.168952 | ||||||||
\(481\) | −24.5078 | −1.11746 | ||||||||
\(482\) | −15.9109 | −0.724723 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00000 | 0.227273 | ||||||||
\(485\) | 23.3141 | 1.05864 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −6.29844 | −0.285409 | −0.142705 | − | 0.989765i | \(-0.545580\pi\) | ||||
−0.142705 | + | 0.989765i | \(0.545580\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | 10.8062 | 0.488675 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.61250 | −0.433806 | −0.216903 | − | 0.976193i | \(-0.569596\pi\) | ||||
−0.216903 | + | 0.976193i | \(0.569596\pi\) | |||||||
\(492\) | −0.298438 | −0.0134546 | ||||||||
\(493\) | −1.19375 | −0.0537639 | ||||||||
\(494\) | 30.8062 | 1.38604 | ||||||||
\(495\) | 14.8062 | 0.665491 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −13.4031 | −0.600608 | ||||||||
\(499\) | −23.4031 | −1.04767 | −0.523834 | − | 0.851820i | \(-0.675499\pi\) | ||||
−0.523834 | + | 0.851820i | \(0.675499\pi\) | |||||||
\(500\) | −13.7016 | −0.612752 | ||||||||
\(501\) | −13.4031 | −0.598807 | ||||||||
\(502\) | 19.7016 | 0.879324 | ||||||||
\(503\) | −4.59688 | −0.204965 | −0.102482 | − | 0.994735i | \(-0.532678\pi\) | ||||
−0.102482 | + | 0.994735i | \(0.532678\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.5969 | −0.560554 | ||||||||
\(506\) | 4.00000 | 0.177822 | ||||||||
\(507\) | −19.5078 | −0.866372 | ||||||||
\(508\) | −5.70156 | −0.252966 | ||||||||
\(509\) | −37.6125 | −1.66714 | −0.833572 | − | 0.552410i | \(-0.813708\pi\) | ||||
−0.833572 | + | 0.552410i | \(0.813708\pi\) | |||||||
\(510\) | 14.8062 | 0.655632 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.40312 | −0.238554 | ||||||||
\(514\) | 2.00000 | 0.0882162 | ||||||||
\(515\) | 8.50781 | 0.374899 | ||||||||
\(516\) | 1.70156 | 0.0749071 | ||||||||
\(517\) | −44.4187 | −1.95353 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.4031 | 0.851703 | ||||||||
\(520\) | −21.1047 | −0.925502 | ||||||||
\(521\) | 20.5969 | 0.902366 | 0.451183 | − | 0.892432i | \(-0.351002\pi\) | ||||
0.451183 | + | 0.892432i | \(0.351002\pi\) | |||||||
\(522\) | −0.298438 | −0.0130623 | ||||||||
\(523\) | −20.8062 | −0.909794 | −0.454897 | − | 0.890544i | \(-0.650324\pi\) | ||||
−0.454897 | + | 0.890544i | \(0.650324\pi\) | |||||||
\(524\) | 7.40312 | 0.323407 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.70156 | −0.423008 | ||||||||
\(527\) | −8.00000 | −0.348485 | ||||||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −34.8062 | −1.51189 | ||||||||
\(531\) | 7.40312 | 0.321268 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.70156 | −0.0737028 | ||||||||
\(534\) | 11.4031 | 0.493461 | ||||||||
\(535\) | −69.6125 | −3.00961 | ||||||||
\(536\) | −14.8062 | −0.639533 | ||||||||
\(537\) | 25.1047 | 1.08335 | ||||||||
\(538\) | −10.2094 | −0.440157 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.70156 | 0.159290 | ||||||||
\(541\) | 33.4031 | 1.43611 | 0.718056 | − | 0.695985i | \(-0.245032\pi\) | ||||
0.718056 | + | 0.695985i | \(0.245032\pi\) | |||||||
\(542\) | 1.40312 | 0.0602693 | ||||||||
\(543\) | −16.8062 | −0.721225 | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | 28.5078 | 1.22114 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.0156 | 1.24062 | 0.620309 | − | 0.784357i | \(-0.287007\pi\) | ||||
0.620309 | + | 0.784357i | \(0.287007\pi\) | |||||||
\(548\) | −19.7016 | −0.841609 | ||||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | 34.8062 | 1.48414 | ||||||||
\(551\) | 1.61250 | 0.0686947 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.4031 | 0.909332 | ||||||||
\(555\) | 15.9109 | 0.675382 | ||||||||
\(556\) | −17.7016 | −0.750713 | ||||||||
\(557\) | −37.4031 | −1.58482 | −0.792411 | − | 0.609988i | \(-0.791174\pi\) | ||||
−0.792411 | + | 0.609988i | \(0.791174\pi\) | |||||||
\(558\) | −2.00000 | −0.0846668 | ||||||||
\(559\) | 9.70156 | 0.410332 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.0000 | −0.675521 | ||||||||
\(562\) | −14.5078 | −0.611975 | ||||||||
\(563\) | 3.10469 | 0.130847 | 0.0654235 | − | 0.997858i | \(-0.479160\pi\) | ||||
0.0654235 | + | 0.997858i | \(0.479160\pi\) | |||||||
\(564\) | −11.1047 | −0.467592 | ||||||||
\(565\) | −26.2984 | −1.10638 | ||||||||
\(566\) | 4.80625 | 0.202022 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.40312 | 0.310628 | ||||||||
\(569\) | 31.7016 | 1.32900 | 0.664499 | − | 0.747289i | \(-0.268645\pi\) | ||||
0.664499 | + | 0.747289i | \(0.268645\pi\) | |||||||
\(570\) | −20.0000 | −0.837708 | ||||||||
\(571\) | −14.8062 | −0.619622 | −0.309811 | − | 0.950798i | \(-0.600266\pi\) | ||||
−0.309811 | + | 0.950798i | \(0.600266\pi\) | |||||||
\(572\) | 22.8062 | 0.953577 | ||||||||
\(573\) | −22.8062 | −0.952745 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.70156 | 0.362880 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 10.0000 | 0.416305 | 0.208153 | − | 0.978096i | \(-0.433255\pi\) | ||||
0.208153 | + | 0.978096i | \(0.433255\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 23.1047 | 0.960198 | ||||||||
\(580\) | −1.10469 | −0.0458696 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.29844 | −0.261079 | ||||||||
\(583\) | 37.6125 | 1.55775 | ||||||||
\(584\) | 1.40312 | 0.0580617 | ||||||||
\(585\) | 21.1047 | 0.872571 | ||||||||
\(586\) | −20.8062 | −0.859498 | ||||||||
\(587\) | −14.8062 | −0.611119 | −0.305560 | − | 0.952173i | \(-0.598844\pi\) | ||||
−0.305560 | + | 0.952173i | \(0.598844\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.8062 | 0.445264 | ||||||||
\(590\) | 27.4031 | 1.12817 | ||||||||
\(591\) | −22.5078 | −0.925848 | ||||||||
\(592\) | 4.29844 | 0.176665 | ||||||||
\(593\) | −43.7016 | −1.79461 | −0.897304 | − | 0.441413i | \(-0.854477\pi\) | ||||
−0.897304 | + | 0.441413i | \(0.854477\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −20.2094 | −0.827808 | ||||||||
\(597\) | −2.29844 | −0.0940688 | ||||||||
\(598\) | 5.70156 | 0.233154 | ||||||||
\(599\) | 13.6125 | 0.556192 | 0.278096 | − | 0.960553i | \(-0.410297\pi\) | ||||
0.278096 | + | 0.960553i | \(0.410297\pi\) | |||||||
\(600\) | 8.70156 | 0.355240 | ||||||||
\(601\) | 13.4031 | 0.546725 | 0.273362 | − | 0.961911i | \(-0.411864\pi\) | ||||
0.273362 | + | 0.961911i | \(0.411864\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.8062 | 0.602957 | ||||||||
\(604\) | 23.9109 | 0.972922 | ||||||||
\(605\) | −18.5078 | −0.752450 | ||||||||
\(606\) | 3.40312 | 0.138242 | ||||||||
\(607\) | 39.6125 | 1.60782 | 0.803911 | − | 0.594750i | \(-0.202749\pi\) | ||||
0.803911 | + | 0.594750i | \(0.202749\pi\) | |||||||
\(608\) | −5.40312 | −0.219126 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.40312 | 0.299744 | ||||||||
\(611\) | −63.3141 | −2.56141 | ||||||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | 3.70156 | 0.149505 | 0.0747523 | − | 0.997202i | \(-0.476183\pi\) | ||||
0.0747523 | + | 0.997202i | \(0.476183\pi\) | |||||||
\(614\) | 11.9109 | 0.480686 | ||||||||
\(615\) | 1.10469 | 0.0445453 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.1938 | −0.772711 | −0.386356 | − | 0.922350i | \(-0.626266\pi\) | ||||
−0.386356 | + | 0.922350i | \(0.626266\pi\) | |||||||
\(618\) | −2.29844 | −0.0924567 | ||||||||
\(619\) | 7.19375 | 0.289141 | 0.144571 | − | 0.989494i | \(-0.453820\pi\) | ||||
0.144571 | + | 0.989494i | \(0.453820\pi\) | |||||||
\(620\) | −7.40312 | −0.297317 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 13.4031 | 0.537416 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.70156 | 0.228245 | ||||||||
\(625\) | 7.20937 | 0.288375 | ||||||||
\(626\) | −6.20937 | −0.248176 | ||||||||
\(627\) | 21.6125 | 0.863120 | ||||||||
\(628\) | 1.40312 | 0.0559908 | ||||||||
\(629\) | −17.1938 | −0.685560 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.6125 | −1.17885 | −0.589427 | − | 0.807821i | \(-0.700647\pi\) | ||||
−0.589427 | + | 0.807821i | \(0.700647\pi\) | |||||||
\(632\) | −8.00000 | −0.318223 | ||||||||
\(633\) | −10.8062 | −0.429510 | ||||||||
\(634\) | 8.29844 | 0.329573 | ||||||||
\(635\) | 21.1047 | 0.837514 | ||||||||
\(636\) | 9.40312 | 0.372858 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.19375 | 0.0472611 | ||||||||
\(639\) | −7.40312 | −0.292863 | ||||||||
\(640\) | 3.70156 | 0.146317 | ||||||||
\(641\) | −20.7172 | −0.818280 | −0.409140 | − | 0.912472i | \(-0.634171\pi\) | ||||
−0.409140 | + | 0.912472i | \(0.634171\pi\) | |||||||
\(642\) | 18.8062 | 0.742223 | ||||||||
\(643\) | −0.806248 | −0.0317953 | −0.0158977 | − | 0.999874i | \(-0.505061\pi\) | ||||
−0.0158977 | + | 0.999874i | \(0.505061\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.29844 | −0.248001 | ||||||||
\(646\) | 21.6125 | 0.850332 | ||||||||
\(647\) | 6.59688 | 0.259350 | 0.129675 | − | 0.991557i | \(-0.458607\pi\) | ||||
0.129675 | + | 0.991557i | \(0.458607\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −29.6125 | −1.16239 | ||||||||
\(650\) | 49.6125 | 1.94596 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.8062 | −0.423205 | ||||||||
\(653\) | 7.10469 | 0.278028 | 0.139014 | − | 0.990290i | \(-0.455607\pi\) | ||||
0.139014 | + | 0.990290i | \(0.455607\pi\) | |||||||
\(654\) | −7.70156 | −0.301155 | ||||||||
\(655\) | −27.4031 | −1.07073 | ||||||||
\(656\) | 0.298438 | 0.0116520 | ||||||||
\(657\) | −1.40312 | −0.0547411 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.00000 | 0.311636 | 0.155818 | − | 0.987786i | \(-0.450199\pi\) | ||||
0.155818 | + | 0.987786i | \(0.450199\pi\) | |||||||
\(660\) | −14.8062 | −0.576332 | ||||||||
\(661\) | −42.4187 | −1.64990 | −0.824949 | − | 0.565207i | \(-0.808796\pi\) | ||||
−0.824949 | + | 0.565207i | \(0.808796\pi\) | |||||||
\(662\) | 20.0000 | 0.777322 | ||||||||
\(663\) | −22.8062 | −0.885721 | ||||||||
\(664\) | 13.4031 | 0.520142 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.29844 | −0.166561 | ||||||||
\(667\) | 0.298438 | 0.0115556 | ||||||||
\(668\) | 13.4031 | 0.518582 | ||||||||
\(669\) | −22.0000 | −0.850569 | ||||||||
\(670\) | 54.8062 | 2.11735 | ||||||||
\(671\) | −8.00000 | −0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.70156 | 0.296873 | 0.148437 | − | 0.988922i | \(-0.452576\pi\) | ||||
0.148437 | + | 0.988922i | \(0.452576\pi\) | |||||||
\(674\) | 4.20937 | 0.162139 | ||||||||
\(675\) | −8.70156 | −0.334923 | ||||||||
\(676\) | 19.5078 | 0.750300 | ||||||||
\(677\) | 50.4187 | 1.93775 | 0.968875 | − | 0.247551i | \(-0.0796257\pi\) | ||||
0.968875 | + | 0.247551i | \(0.0796257\pi\) | |||||||
\(678\) | 7.10469 | 0.272854 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −14.8062 | −0.567794 | ||||||||
\(681\) | −23.1047 | −0.885374 | ||||||||
\(682\) | 8.00000 | 0.306336 | ||||||||
\(683\) | 33.6125 | 1.28615 | 0.643073 | − | 0.765805i | \(-0.277659\pi\) | ||||
0.643073 | + | 0.765805i | \(0.277659\pi\) | |||||||
\(684\) | 5.40312 | 0.206594 | ||||||||
\(685\) | 72.9266 | 2.78638 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.5969 | −0.556906 | ||||||||
\(688\) | −1.70156 | −0.0648714 | ||||||||
\(689\) | 53.6125 | 2.04247 | ||||||||
\(690\) | −3.70156 | −0.140916 | ||||||||
\(691\) | 0.507811 | 0.0193180 | 0.00965901 | − | 0.999953i | \(-0.496925\pi\) | ||||
0.00965901 | + | 0.999953i | \(0.496925\pi\) | |||||||
\(692\) | −19.4031 | −0.737596 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.2984 | 0.390923 | ||||||||
\(695\) | 65.5234 | 2.48545 | ||||||||
\(696\) | 0.298438 | 0.0113123 | ||||||||
\(697\) | −1.19375 | −0.0452166 | ||||||||
\(698\) | 12.5969 | 0.476799 | ||||||||
\(699\) | 26.0000 | 0.983410 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.0156 | 1.77576 | 0.887878 | − | 0.460079i | \(-0.152179\pi\) | ||||
0.887878 | + | 0.460079i | \(0.152179\pi\) | |||||||
\(702\) | −5.70156 | −0.215192 | ||||||||
\(703\) | 23.2250 | 0.875947 | ||||||||
\(704\) | −4.00000 | −0.150756 | ||||||||
\(705\) | 41.1047 | 1.54809 | ||||||||
\(706\) | 4.29844 | 0.161774 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.40312 | −0.278226 | ||||||||
\(709\) | 23.1938 | 0.871060 | 0.435530 | − | 0.900174i | \(-0.356561\pi\) | ||||
0.435530 | + | 0.900174i | \(0.356561\pi\) | |||||||
\(710\) | −27.4031 | −1.02842 | ||||||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | −11.4031 | −0.427350 | ||||||||
\(713\) | 2.00000 | 0.0749006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −84.4187 | −3.15708 | ||||||||
\(716\) | −25.1047 | −0.938206 | ||||||||
\(717\) | −10.8062 | −0.403567 | ||||||||
\(718\) | 2.89531 | 0.108052 | ||||||||
\(719\) | 5.91093 | 0.220441 | 0.110220 | − | 0.993907i | \(-0.464844\pi\) | ||||
0.110220 | + | 0.993907i | \(0.464844\pi\) | |||||||
\(720\) | −3.70156 | −0.137949 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.1938 | −0.379372 | ||||||||
\(723\) | −15.9109 | −0.591734 | ||||||||
\(724\) | 16.8062 | 0.624599 | ||||||||
\(725\) | 2.59688 | 0.0964455 | ||||||||
\(726\) | 5.00000 | 0.185567 | ||||||||
\(727\) | 12.0000 | 0.445055 | 0.222528 | − | 0.974926i | \(-0.428569\pi\) | ||||
0.222528 | + | 0.974926i | \(0.428569\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.19375 | −0.192229 | ||||||||
\(731\) | 6.80625 | 0.251738 | ||||||||
\(732\) | −2.00000 | −0.0739221 | ||||||||
\(733\) | −52.2094 | −1.92840 | −0.964199 | − | 0.265181i | \(-0.914568\pi\) | ||||
−0.964199 | + | 0.265181i | \(0.914568\pi\) | |||||||
\(734\) | −17.1047 | −0.631345 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −59.2250 | −2.18158 | ||||||||
\(738\) | −0.298438 | −0.0109857 | ||||||||
\(739\) | −29.0156 | −1.06736 | −0.533678 | − | 0.845687i | \(-0.679191\pi\) | ||||
−0.533678 | + | 0.845687i | \(0.679191\pi\) | |||||||
\(740\) | −15.9109 | −0.584898 | ||||||||
\(741\) | 30.8062 | 1.13170 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.0000 | 1.17397 | 0.586983 | − | 0.809599i | \(-0.300316\pi\) | ||||
0.586983 | + | 0.809599i | \(0.300316\pi\) | |||||||
\(744\) | 2.00000 | 0.0733236 | ||||||||
\(745\) | 74.8062 | 2.74069 | ||||||||
\(746\) | 0.806248 | 0.0295189 | ||||||||
\(747\) | −13.4031 | −0.490395 | ||||||||
\(748\) | 16.0000 | 0.585018 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −13.7016 | −0.500310 | ||||||||
\(751\) | 29.6125 | 1.08058 | 0.540288 | − | 0.841480i | \(-0.318315\pi\) | ||||
0.540288 | + | 0.841480i | \(0.318315\pi\) | |||||||
\(752\) | 11.1047 | 0.404946 | ||||||||
\(753\) | 19.7016 | 0.717965 | ||||||||
\(754\) | 1.70156 | 0.0619672 | ||||||||
\(755\) | −88.5078 | −3.22113 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.4187 | −0.960206 | −0.480103 | − | 0.877212i | \(-0.659401\pi\) | ||||
−0.480103 | + | 0.877212i | \(0.659401\pi\) | |||||||
\(758\) | −13.7016 | −0.497663 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 20.0000 | 0.725476 | ||||||||
\(761\) | 35.6125 | 1.29095 | 0.645476 | − | 0.763781i | \(-0.276659\pi\) | ||||
0.645476 | + | 0.763781i | \(0.276659\pi\) | |||||||
\(762\) | −5.70156 | −0.206546 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 22.8062 | 0.825101 | ||||||||
\(765\) | 14.8062 | 0.535321 | ||||||||
\(766\) | 29.6125 | 1.06994 | ||||||||
\(767\) | −42.2094 | −1.52409 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −15.9109 | −0.573763 | −0.286881 | − | 0.957966i | \(-0.592619\pi\) | ||||
−0.286881 | + | 0.957966i | \(0.592619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.00000 | 0.0720282 | ||||||||
\(772\) | −23.1047 | −0.831556 | ||||||||
\(773\) | 7.10469 | 0.255538 | 0.127769 | − | 0.991804i | \(-0.459218\pi\) | ||||
0.127769 | + | 0.991804i | \(0.459218\pi\) | |||||||
\(774\) | 1.70156 | 0.0611614 | ||||||||
\(775\) | 17.4031 | 0.625139 | ||||||||
\(776\) | 6.29844 | 0.226101 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000 | 0.215110 | ||||||||
\(779\) | 1.61250 | 0.0577737 | ||||||||
\(780\) | −21.1047 | −0.755669 | ||||||||
\(781\) | 29.6125 | 1.05962 | ||||||||
\(782\) | 4.00000 | 0.143040 | ||||||||
\(783\) | −0.298438 | −0.0106653 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.19375 | −0.185373 | ||||||||
\(786\) | 7.40312 | 0.264061 | ||||||||
\(787\) | 18.5969 | 0.662907 | 0.331454 | − | 0.943472i | \(-0.392461\pi\) | ||||
0.331454 | + | 0.943472i | \(0.392461\pi\) | |||||||
\(788\) | 22.5078 | 0.801808 | ||||||||
\(789\) | −9.70156 | −0.345385 | ||||||||
\(790\) | 29.6125 | 1.05357 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.00000 | 0.142134 | ||||||||
\(793\) | −11.4031 | −0.404937 | ||||||||
\(794\) | 8.59688 | 0.305092 | ||||||||
\(795\) | −34.8062 | −1.23445 | ||||||||
\(796\) | 2.29844 | 0.0814660 | ||||||||
\(797\) | −15.7016 | −0.556178 | −0.278089 | − | 0.960555i | \(-0.589701\pi\) | ||||
−0.278089 | + | 0.960555i | \(0.589701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.4187 | −1.57142 | ||||||||
\(800\) | −8.70156 | −0.307647 | ||||||||
\(801\) | 11.4031 | 0.402910 | ||||||||
\(802\) | −30.0000 | −1.05934 | ||||||||
\(803\) | 5.61250 | 0.198061 | ||||||||
\(804\) | −14.8062 | −0.522176 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.4031 | 0.401658 | ||||||||
\(807\) | −10.2094 | −0.359387 | ||||||||
\(808\) | −3.40312 | −0.119721 | ||||||||
\(809\) | 31.0156 | 1.09045 | 0.545226 | − | 0.838289i | \(-0.316444\pi\) | ||||
0.545226 | + | 0.838289i | \(0.316444\pi\) | |||||||
\(810\) | 3.70156 | 0.130060 | ||||||||
\(811\) | −52.5078 | −1.84380 | −0.921899 | − | 0.387430i | \(-0.873363\pi\) | ||||
−0.921899 | + | 0.387430i | \(0.873363\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.40312 | 0.0492097 | ||||||||
\(814\) | 17.1938 | 0.602641 | ||||||||
\(815\) | 40.0000 | 1.40114 | ||||||||
\(816\) | 4.00000 | 0.140028 | ||||||||
\(817\) | −9.19375 | −0.321649 | ||||||||
\(818\) | 5.40312 | 0.188916 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.10469 | −0.0385773 | ||||||||
\(821\) | 27.6125 | 0.963683 | 0.481841 | − | 0.876258i | \(-0.339968\pi\) | ||||
0.481841 | + | 0.876258i | \(0.339968\pi\) | |||||||
\(822\) | −19.7016 | −0.687171 | ||||||||
\(823\) | −13.7016 | −0.477606 | −0.238803 | − | 0.971068i | \(-0.576755\pi\) | ||||
−0.238803 | + | 0.971068i | \(0.576755\pi\) | |||||||
\(824\) | 2.29844 | 0.0800699 | ||||||||
\(825\) | 34.8062 | 1.21180 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.4031 | −1.64837 | −0.824184 | − | 0.566322i | \(-0.808366\pi\) | ||||
−0.824184 | + | 0.566322i | \(0.808366\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −55.4031 | −1.92423 | −0.962115 | − | 0.272644i | \(-0.912102\pi\) | ||||
−0.962115 | + | 0.272644i | \(0.912102\pi\) | |||||||
\(830\) | −49.6125 | −1.72207 | ||||||||
\(831\) | 21.4031 | 0.742466 | ||||||||
\(832\) | −5.70156 | −0.197666 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −17.7016 | −0.612955 | ||||||||
\(835\) | −49.6125 | −1.71691 | ||||||||
\(836\) | −21.6125 | −0.747484 | ||||||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | −0.209373 | −0.00723266 | ||||||||
\(839\) | −42.2094 | −1.45723 | −0.728615 | − | 0.684924i | \(-0.759835\pi\) | ||||
−0.728615 | + | 0.684924i | \(0.759835\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9109 | −0.996929 | ||||||||
\(842\) | 15.7016 | 0.541112 | ||||||||
\(843\) | −14.5078 | −0.499676 | ||||||||
\(844\) | 10.8062 | 0.371966 | ||||||||
\(845\) | −72.2094 | −2.48408 | ||||||||
\(846\) | −11.1047 | −0.381787 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.40312 | −0.322905 | ||||||||
\(849\) | 4.80625 | 0.164950 | ||||||||
\(850\) | 34.8062 | 1.19384 | ||||||||
\(851\) | 4.29844 | 0.147349 | ||||||||
\(852\) | 7.40312 | 0.253627 | ||||||||
\(853\) | −9.10469 | −0.311739 | −0.155869 | − | 0.987778i | \(-0.549818\pi\) | ||||
−0.155869 | + | 0.987778i | \(0.549818\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.0000 | −0.683986 | ||||||||
\(856\) | −18.8062 | −0.642784 | ||||||||
\(857\) | 0.298438 | 0.0101944 | 0.00509722 | − | 0.999987i | \(-0.498377\pi\) | ||||
0.00509722 | + | 0.999987i | \(0.498377\pi\) | |||||||
\(858\) | 22.8062 | 0.778592 | ||||||||
\(859\) | 15.4922 | 0.528587 | 0.264293 | − | 0.964442i | \(-0.414861\pi\) | ||||
0.264293 | + | 0.964442i | \(0.414861\pi\) | |||||||
\(860\) | 6.29844 | 0.214775 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.91093 | 0.133207 | ||||||||
\(863\) | −6.38750 | −0.217433 | −0.108717 | − | 0.994073i | \(-0.534674\pi\) | ||||
−0.108717 | + | 0.994073i | \(0.534674\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 71.8219 | 2.44202 | ||||||||
\(866\) | 31.3141 | 1.06410 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.0000 | −1.08553 | ||||||||
\(870\) | −1.10469 | −0.0374524 | ||||||||
\(871\) | −84.4187 | −2.86042 | ||||||||
\(872\) | 7.70156 | 0.260808 | ||||||||
\(873\) | −6.29844 | −0.213170 | ||||||||
\(874\) | −5.40312 | −0.182763 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.40312 | 0.0474072 | ||||||||
\(877\) | −17.4031 | −0.587662 | −0.293831 | − | 0.955857i | \(-0.594930\pi\) | ||||
−0.293831 | + | 0.955857i | \(0.594930\pi\) | |||||||
\(878\) | −22.0000 | −0.742464 | ||||||||
\(879\) | −20.8062 | −0.701777 | ||||||||
\(880\) | 14.8062 | 0.499119 | ||||||||
\(881\) | −6.20937 | −0.209199 | −0.104600 | − | 0.994514i | \(-0.533356\pi\) | ||||
−0.104600 | + | 0.994514i | \(0.533356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.5969 | −0.827751 | −0.413875 | − | 0.910334i | \(-0.635825\pi\) | ||||
−0.413875 | + | 0.910334i | \(0.635825\pi\) | |||||||
\(884\) | 22.8062 | 0.767057 | ||||||||
\(885\) | 27.4031 | 0.921146 | ||||||||
\(886\) | 13.7016 | 0.460313 | ||||||||
\(887\) | 28.2094 | 0.947178 | 0.473589 | − | 0.880746i | \(-0.342958\pi\) | ||||
0.473589 | + | 0.880746i | \(0.342958\pi\) | |||||||
\(888\) | 4.29844 | 0.144246 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 42.2094 | 1.41486 | ||||||||
\(891\) | −4.00000 | −0.134005 | ||||||||
\(892\) | 22.0000 | 0.736614 | ||||||||
\(893\) | 60.0000 | 2.00782 | ||||||||
\(894\) | −20.2094 | −0.675903 | ||||||||
\(895\) | 92.9266 | 3.10619 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.70156 | 0.190370 | ||||||||
\(898\) | 38.4187 | 1.28205 | ||||||||
\(899\) | 0.596876 | 0.0199069 | ||||||||
\(900\) | 8.70156 | 0.290052 | ||||||||
\(901\) | 37.6125 | 1.25305 | ||||||||
\(902\) | 1.19375 | 0.0397476 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.10469 | −0.236298 | ||||||||
\(905\) | −62.2094 | −2.06791 | ||||||||
\(906\) | 23.9109 | 0.794388 | ||||||||
\(907\) | 20.5078 | 0.680951 | 0.340475 | − | 0.940253i | \(-0.389412\pi\) | ||||
0.340475 | + | 0.940253i | \(0.389412\pi\) | |||||||
\(908\) | 23.1047 | 0.766756 | ||||||||
\(909\) | 3.40312 | 0.112875 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.1047 | 1.75944 | 0.879718 | − | 0.475495i | \(-0.157731\pi\) | ||||
0.879718 | + | 0.475495i | \(0.157731\pi\) | |||||||
\(912\) | −5.40312 | −0.178915 | ||||||||
\(913\) | 53.6125 | 1.77431 | ||||||||
\(914\) | −28.2094 | −0.933083 | ||||||||
\(915\) | 7.40312 | 0.244740 | ||||||||
\(916\) | 14.5969 | 0.482294 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.00000 | −0.132020 | ||||||||
\(919\) | −52.4187 | −1.72913 | −0.864567 | − | 0.502517i | \(-0.832407\pi\) | ||||
−0.864567 | + | 0.502517i | \(0.832407\pi\) | |||||||
\(920\) | 3.70156 | 0.122037 | ||||||||
\(921\) | 11.9109 | 0.392479 | ||||||||
\(922\) | −2.20937 | −0.0727618 | ||||||||
\(923\) | 42.2094 | 1.38934 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.4031 | 1.22981 | ||||||||
\(926\) | 22.2984 | 0.732772 | ||||||||
\(927\) | −2.29844 | −0.0754906 | ||||||||
\(928\) | −0.298438 | −0.00979670 | ||||||||
\(929\) | 45.9109 | 1.50629 | 0.753144 | − | 0.657855i | \(-0.228536\pi\) | ||||
0.753144 | + | 0.657855i | \(0.228536\pi\) | |||||||
\(930\) | −7.40312 | −0.242758 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −26.0000 | −0.851658 | ||||||||
\(933\) | 13.4031 | 0.438799 | ||||||||
\(934\) | −3.70156 | −0.121119 | ||||||||
\(935\) | −59.2250 | −1.93686 | ||||||||
\(936\) | 5.70156 | 0.186361 | ||||||||
\(937\) | −25.1047 | −0.820134 | −0.410067 | − | 0.912055i | \(-0.634495\pi\) | ||||
−0.410067 | + | 0.912055i | \(0.634495\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.20937 | −0.202635 | ||||||||
\(940\) | −41.1047 | −1.34069 | ||||||||
\(941\) | −25.3141 | −0.825215 | −0.412607 | − | 0.910909i | \(-0.635382\pi\) | ||||
−0.412607 | + | 0.910909i | \(0.635382\pi\) | |||||||
\(942\) | 1.40312 | 0.0457163 | ||||||||
\(943\) | 0.298438 | 0.00971847 | ||||||||
\(944\) | 7.40312 | 0.240951 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.80625 | −0.221290 | ||||||||
\(947\) | 15.9109 | 0.517036 | 0.258518 | − | 0.966006i | \(-0.416766\pi\) | ||||
0.258518 | + | 0.966006i | \(0.416766\pi\) | |||||||
\(948\) | −8.00000 | −0.259828 | ||||||||
\(949\) | 8.00000 | 0.259691 | ||||||||
\(950\) | −47.0156 | −1.52539 | ||||||||
\(951\) | 8.29844 | 0.269095 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 61.2250 | 1.98327 | 0.991636 | − | 0.129066i | \(-0.0411978\pi\) | ||||
0.991636 | + | 0.129066i | \(0.0411978\pi\) | |||||||
\(954\) | 9.40312 | 0.304437 | ||||||||
\(955\) | −84.4187 | −2.73173 | ||||||||
\(956\) | 10.8062 | 0.349499 | ||||||||
\(957\) | 1.19375 | 0.0385885 | ||||||||
\(958\) | 16.5969 | 0.536221 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.70156 | 0.119467 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 24.5078 | 0.790164 | ||||||||
\(963\) | 18.8062 | 0.606023 | ||||||||
\(964\) | 15.9109 | 0.512457 | ||||||||
\(965\) | 85.5234 | 2.75310 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.8062 | −0.476137 | −0.238068 | − | 0.971248i | \(-0.576514\pi\) | ||||
−0.238068 | + | 0.971248i | \(0.576514\pi\) | |||||||
\(968\) | −5.00000 | −0.160706 | ||||||||
\(969\) | 21.6125 | 0.694293 | ||||||||
\(970\) | −23.3141 | −0.748569 | ||||||||
\(971\) | −49.8219 | −1.59886 | −0.799430 | − | 0.600759i | \(-0.794865\pi\) | ||||
−0.799430 | + | 0.600759i | \(0.794865\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6.29844 | 0.201815 | ||||||||
\(975\) | 49.6125 | 1.58887 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 16.7172 | 0.534830 | 0.267415 | − | 0.963581i | \(-0.413831\pi\) | ||||
0.267415 | + | 0.963581i | \(0.413831\pi\) | |||||||
\(978\) | −10.8062 | −0.345546 | ||||||||
\(979\) | −45.6125 | −1.45778 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.70156 | −0.245892 | ||||||||
\(982\) | 9.61250 | 0.306747 | ||||||||
\(983\) | −42.2094 | −1.34627 | −0.673135 | − | 0.739520i | \(-0.735053\pi\) | ||||
−0.673135 | + | 0.739520i | \(0.735053\pi\) | |||||||
\(984\) | 0.298438 | 0.00951385 | ||||||||
\(985\) | −83.3141 | −2.65461 | ||||||||
\(986\) | 1.19375 | 0.0380168 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −30.8062 | −0.980077 | ||||||||
\(989\) | −1.70156 | −0.0541065 | ||||||||
\(990\) | −14.8062 | −0.470573 | ||||||||
\(991\) | 28.0000 | 0.889449 | 0.444725 | − | 0.895667i | \(-0.353302\pi\) | ||||
0.444725 | + | 0.895667i | \(0.353302\pi\) | |||||||
\(992\) | −2.00000 | −0.0635001 | ||||||||
\(993\) | 20.0000 | 0.634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.50781 | −0.269716 | ||||||||
\(996\) | 13.4031 | 0.424694 | ||||||||
\(997\) | 23.4031 | 0.741184 | 0.370592 | − | 0.928796i | \(-0.379155\pi\) | ||||
0.370592 | + | 0.928796i | \(0.379155\pi\) | |||||||
\(998\) | 23.4031 | 0.740813 | ||||||||
\(999\) | −4.29844 | −0.135997 |
(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 | 6762.2.a.bo.1.1 | 2 | ||
7.6 | odd | 2 | 966.2.a.n.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 2898.2.a.bb.1.1 | 2 | |||
28.27 | even | 2 | 7728.2.a.bc.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.a.n.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
2898.2.a.bb.1.1 | 2 | 21.20 | even | 2 | |||
6762.2.a.bo.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7728.2.a.bc.1.2 | 2 | 28.27 | even | 2 |