Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [285,2,Mod(1,285)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(285, 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("285.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 285 = 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 285.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: | \(2.27573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 285.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | −1.22474 | −0.612372 | − | 0.790569i | \(-0.709785\pi\) | ||||
−0.612372 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.73205 | −0.707107 | ||||||||
\(7\) | −2.73205 | −1.03262 | −0.516309 | − | 0.856402i | \(-0.672694\pi\) | ||||
−0.516309 | + | 0.856402i | \(0.672694\pi\) | |||||||
\(8\) | 1.73205 | 0.612372 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.73205 | −0.547723 | ||||||||
\(11\) | 4.73205 | 1.42677 | 0.713384 | − | 0.700774i | \(-0.247162\pi\) | ||||
0.713384 | + | 0.700774i | \(0.247162\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0.732051 | 0.203034 | 0.101517 | − | 0.994834i | \(-0.467630\pi\) | ||||
0.101517 | + | 0.994834i | \(0.467630\pi\) | |||||||
\(14\) | 4.73205 | 1.26469 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −1.73205 | −0.408248 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.73205 | −0.596182 | ||||||||
\(22\) | −8.19615 | −1.74743 | ||||||||
\(23\) | 3.46410 | 0.722315 | 0.361158 | − | 0.932505i | \(-0.382382\pi\) | ||||
0.361158 | + | 0.932505i | \(0.382382\pi\) | |||||||
\(24\) | 1.73205 | 0.353553 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.26795 | −0.248665 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.73205 | −0.516309 | ||||||||
\(29\) | 8.19615 | 1.52199 | 0.760994 | − | 0.648759i | \(-0.224712\pi\) | ||||
0.760994 | + | 0.648759i | \(0.224712\pi\) | |||||||
\(30\) | −1.73205 | −0.316228 | ||||||||
\(31\) | 8.92820 | 1.60355 | 0.801776 | − | 0.597624i | \(-0.203889\pi\) | ||||
0.801776 | + | 0.597624i | \(0.203889\pi\) | |||||||
\(32\) | 5.19615 | 0.918559 | ||||||||
\(33\) | 4.73205 | 0.823744 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.73205 | −0.461801 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.19615 | −1.01864 | −0.509321 | − | 0.860577i | \(-0.670103\pi\) | ||||
−0.509321 | + | 0.860577i | \(0.670103\pi\) | |||||||
\(38\) | −1.73205 | −0.280976 | ||||||||
\(39\) | 0.732051 | 0.117222 | ||||||||
\(40\) | 1.73205 | 0.273861 | ||||||||
\(41\) | 1.26795 | 0.198020 | 0.0990102 | − | 0.995086i | \(-0.468432\pi\) | ||||
0.0990102 | + | 0.995086i | \(0.468432\pi\) | |||||||
\(42\) | 4.73205 | 0.730171 | ||||||||
\(43\) | 4.19615 | 0.639907 | 0.319954 | − | 0.947433i | \(-0.396333\pi\) | ||||
0.319954 | + | 0.947433i | \(0.396333\pi\) | |||||||
\(44\) | 4.73205 | 0.713384 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | −3.46410 | −0.505291 | −0.252646 | − | 0.967559i | \(-0.581301\pi\) | ||||
−0.252646 | + | 0.967559i | \(0.581301\pi\) | |||||||
\(48\) | −5.00000 | −0.721688 | ||||||||
\(49\) | 0.464102 | 0.0663002 | ||||||||
\(50\) | −1.73205 | −0.244949 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.732051 | 0.101517 | ||||||||
\(53\) | −9.46410 | −1.29999 | −0.649997 | − | 0.759937i | \(-0.725230\pi\) | ||||
−0.649997 | + | 0.759937i | \(0.725230\pi\) | |||||||
\(54\) | −1.73205 | −0.235702 | ||||||||
\(55\) | 4.73205 | 0.638070 | ||||||||
\(56\) | −4.73205 | −0.632347 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −14.1962 | −1.86405 | ||||||||
\(59\) | 2.53590 | 0.330146 | 0.165073 | − | 0.986281i | \(-0.447214\pi\) | ||||
0.165073 | + | 0.986281i | \(0.447214\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −6.53590 | −0.836836 | −0.418418 | − | 0.908255i | \(-0.637415\pi\) | ||||
−0.418418 | + | 0.908255i | \(0.637415\pi\) | |||||||
\(62\) | −15.4641 | −1.96394 | ||||||||
\(63\) | −2.73205 | −0.344206 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.732051 | 0.0907997 | ||||||||
\(66\) | −8.19615 | −1.00888 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.46410 | 0.417029 | ||||||||
\(70\) | 4.73205 | 0.565588 | ||||||||
\(71\) | −4.39230 | −0.521271 | −0.260635 | − | 0.965437i | \(-0.583932\pi\) | ||||
−0.260635 | + | 0.965437i | \(0.583932\pi\) | |||||||
\(72\) | 1.73205 | 0.204124 | ||||||||
\(73\) | −16.9282 | −1.98130 | −0.990648 | − | 0.136441i | \(-0.956434\pi\) | ||||
−0.990648 | + | 0.136441i | \(0.956434\pi\) | |||||||
\(74\) | 10.7321 | 1.24758 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −12.9282 | −1.47331 | ||||||||
\(78\) | −1.26795 | −0.143567 | ||||||||
\(79\) | −10.9282 | −1.22952 | −0.614759 | − | 0.788715i | \(-0.710747\pi\) | ||||
−0.614759 | + | 0.788715i | \(0.710747\pi\) | |||||||
\(80\) | −5.00000 | −0.559017 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.19615 | −0.242524 | ||||||||
\(83\) | −12.9282 | −1.41905 | −0.709527 | − | 0.704678i | \(-0.751092\pi\) | ||||
−0.709527 | + | 0.704678i | \(0.751092\pi\) | |||||||
\(84\) | −2.73205 | −0.298091 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.26795 | −0.783723 | ||||||||
\(87\) | 8.19615 | 0.878720 | ||||||||
\(88\) | 8.19615 | 0.873713 | ||||||||
\(89\) | 10.7321 | 1.13760 | 0.568798 | − | 0.822478i | \(-0.307409\pi\) | ||||
0.568798 | + | 0.822478i | \(0.307409\pi\) | |||||||
\(90\) | −1.73205 | −0.182574 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 3.46410 | 0.361158 | ||||||||
\(93\) | 8.92820 | 0.925812 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 5.19615 | 0.530330 | ||||||||
\(97\) | −6.19615 | −0.629124 | −0.314562 | − | 0.949237i | \(-0.601858\pi\) | ||||
−0.314562 | + | 0.949237i | \(0.601858\pi\) | |||||||
\(98\) | −0.803848 | −0.0812009 | ||||||||
\(99\) | 4.73205 | 0.475589 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −10.3923 | −1.03407 | −0.517036 | − | 0.855963i | \(-0.672965\pi\) | ||||
−0.517036 | + | 0.855963i | \(0.672965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.85641 | 0.971181 | 0.485590 | − | 0.874187i | \(-0.338605\pi\) | ||||
0.485590 | + | 0.874187i | \(0.338605\pi\) | |||||||
\(104\) | 1.26795 | 0.124333 | ||||||||
\(105\) | −2.73205 | −0.266621 | ||||||||
\(106\) | 16.3923 | 1.59216 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −14.3923 | −1.37853 | −0.689266 | − | 0.724508i | \(-0.742067\pi\) | ||||
−0.689266 | + | 0.724508i | \(0.742067\pi\) | |||||||
\(110\) | −8.19615 | −0.781472 | ||||||||
\(111\) | −6.19615 | −0.588113 | ||||||||
\(112\) | 13.6603 | 1.29077 | ||||||||
\(113\) | 18.9282 | 1.78062 | 0.890308 | − | 0.455359i | \(-0.150489\pi\) | ||||
0.890308 | + | 0.455359i | \(0.150489\pi\) | |||||||
\(114\) | −1.73205 | −0.162221 | ||||||||
\(115\) | 3.46410 | 0.323029 | ||||||||
\(116\) | 8.19615 | 0.760994 | ||||||||
\(117\) | 0.732051 | 0.0676781 | ||||||||
\(118\) | −4.39230 | −0.404344 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.73205 | 0.158114 | ||||||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | 11.3205 | 1.02491 | ||||||||
\(123\) | 1.26795 | 0.114327 | ||||||||
\(124\) | 8.92820 | 0.801776 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 4.73205 | 0.421565 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −12.1244 | −1.07165 | ||||||||
\(129\) | 4.19615 | 0.369451 | ||||||||
\(130\) | −1.26795 | −0.111207 | ||||||||
\(131\) | −9.12436 | −0.797199 | −0.398599 | − | 0.917125i | \(-0.630504\pi\) | ||||
−0.398599 | + | 0.917125i | \(0.630504\pi\) | |||||||
\(132\) | 4.73205 | 0.411872 | ||||||||
\(133\) | −2.73205 | −0.236899 | ||||||||
\(134\) | −13.8564 | −1.19701 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.8564 | 1.69645 | 0.848224 | − | 0.529638i | \(-0.177672\pi\) | ||||
0.848224 | + | 0.529638i | \(0.177672\pi\) | |||||||
\(138\) | −6.00000 | −0.510754 | ||||||||
\(139\) | −8.39230 | −0.711826 | −0.355913 | − | 0.934519i | \(-0.615830\pi\) | ||||
−0.355913 | + | 0.934519i | \(0.615830\pi\) | |||||||
\(140\) | −2.73205 | −0.230900 | ||||||||
\(141\) | −3.46410 | −0.291730 | ||||||||
\(142\) | 7.60770 | 0.638424 | ||||||||
\(143\) | 3.46410 | 0.289683 | ||||||||
\(144\) | −5.00000 | −0.416667 | ||||||||
\(145\) | 8.19615 | 0.680653 | ||||||||
\(146\) | 29.3205 | 2.42658 | ||||||||
\(147\) | 0.464102 | 0.0382785 | ||||||||
\(148\) | −6.19615 | −0.509321 | ||||||||
\(149\) | −19.8564 | −1.62670 | −0.813350 | − | 0.581775i | \(-0.802359\pi\) | ||||
−0.813350 | + | 0.581775i | \(0.802359\pi\) | |||||||
\(150\) | −1.73205 | −0.141421 | ||||||||
\(151\) | 14.0000 | 1.13930 | 0.569652 | − | 0.821886i | \(-0.307078\pi\) | ||||
0.569652 | + | 0.821886i | \(0.307078\pi\) | |||||||
\(152\) | 1.73205 | 0.140488 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 22.3923 | 1.80442 | ||||||||
\(155\) | 8.92820 | 0.717131 | ||||||||
\(156\) | 0.732051 | 0.0586110 | ||||||||
\(157\) | 6.39230 | 0.510161 | 0.255081 | − | 0.966920i | \(-0.417898\pi\) | ||||
0.255081 | + | 0.966920i | \(0.417898\pi\) | |||||||
\(158\) | 18.9282 | 1.50585 | ||||||||
\(159\) | −9.46410 | −0.750552 | ||||||||
\(160\) | 5.19615 | 0.410792 | ||||||||
\(161\) | −9.46410 | −0.745876 | ||||||||
\(162\) | −1.73205 | −0.136083 | ||||||||
\(163\) | 9.26795 | 0.725922 | 0.362961 | − | 0.931804i | \(-0.381766\pi\) | ||||
0.362961 | + | 0.931804i | \(0.381766\pi\) | |||||||
\(164\) | 1.26795 | 0.0990102 | ||||||||
\(165\) | 4.73205 | 0.368390 | ||||||||
\(166\) | 22.3923 | 1.73798 | ||||||||
\(167\) | 3.46410 | 0.268060 | 0.134030 | − | 0.990977i | \(-0.457208\pi\) | ||||
0.134030 | + | 0.990977i | \(0.457208\pi\) | |||||||
\(168\) | −4.73205 | −0.365086 | ||||||||
\(169\) | −12.4641 | −0.958777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 4.19615 | 0.319954 | ||||||||
\(173\) | 6.92820 | 0.526742 | 0.263371 | − | 0.964695i | \(-0.415166\pi\) | ||||
0.263371 | + | 0.964695i | \(0.415166\pi\) | |||||||
\(174\) | −14.1962 | −1.07621 | ||||||||
\(175\) | −2.73205 | −0.206524 | ||||||||
\(176\) | −23.6603 | −1.78346 | ||||||||
\(177\) | 2.53590 | 0.190610 | ||||||||
\(178\) | −18.5885 | −1.39326 | ||||||||
\(179\) | 23.3205 | 1.74306 | 0.871528 | − | 0.490345i | \(-0.163129\pi\) | ||||
0.871528 | + | 0.490345i | \(0.163129\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −2.39230 | −0.177819 | −0.0889093 | − | 0.996040i | \(-0.528338\pi\) | ||||
−0.0889093 | + | 0.996040i | \(0.528338\pi\) | |||||||
\(182\) | 3.46410 | 0.256776 | ||||||||
\(183\) | −6.53590 | −0.483148 | ||||||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | −6.19615 | −0.455550 | ||||||||
\(186\) | −15.4641 | −1.13388 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.46410 | −0.252646 | ||||||||
\(189\) | −2.73205 | −0.198727 | ||||||||
\(190\) | −1.73205 | −0.125656 | ||||||||
\(191\) | 0.339746 | 0.0245832 | 0.0122916 | − | 0.999924i | \(-0.496087\pi\) | ||||
0.0122916 | + | 0.999924i | \(0.496087\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 17.1244 | 1.23264 | 0.616319 | − | 0.787497i | \(-0.288623\pi\) | ||||
0.616319 | + | 0.787497i | \(0.288623\pi\) | |||||||
\(194\) | 10.7321 | 0.770516 | ||||||||
\(195\) | 0.732051 | 0.0524232 | ||||||||
\(196\) | 0.464102 | 0.0331501 | ||||||||
\(197\) | −24.0000 | −1.70993 | −0.854965 | − | 0.518686i | \(-0.826421\pi\) | ||||
−0.854965 | + | 0.518686i | \(0.826421\pi\) | |||||||
\(198\) | −8.19615 | −0.582475 | ||||||||
\(199\) | −15.3205 | −1.08604 | −0.543021 | − | 0.839719i | \(-0.682720\pi\) | ||||
−0.543021 | + | 0.839719i | \(0.682720\pi\) | |||||||
\(200\) | 1.73205 | 0.122474 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 18.0000 | 1.26648 | ||||||||
\(203\) | −22.3923 | −1.57163 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.26795 | 0.0885574 | ||||||||
\(206\) | −17.0718 | −1.18945 | ||||||||
\(207\) | 3.46410 | 0.240772 | ||||||||
\(208\) | −3.66025 | −0.253793 | ||||||||
\(209\) | 4.73205 | 0.327323 | ||||||||
\(210\) | 4.73205 | 0.326543 | ||||||||
\(211\) | 1.07180 | 0.0737855 | 0.0368928 | − | 0.999319i | \(-0.488254\pi\) | ||||
0.0368928 | + | 0.999319i | \(0.488254\pi\) | |||||||
\(212\) | −9.46410 | −0.649997 | ||||||||
\(213\) | −4.39230 | −0.300956 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.19615 | 0.286175 | ||||||||
\(216\) | 1.73205 | 0.117851 | ||||||||
\(217\) | −24.3923 | −1.65586 | ||||||||
\(218\) | 24.9282 | 1.68835 | ||||||||
\(219\) | −16.9282 | −1.14390 | ||||||||
\(220\) | 4.73205 | 0.319035 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 10.7321 | 0.720288 | ||||||||
\(223\) | −17.8564 | −1.19575 | −0.597877 | − | 0.801588i | \(-0.703989\pi\) | ||||
−0.597877 | + | 0.801588i | \(0.703989\pi\) | |||||||
\(224\) | −14.1962 | −0.948520 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −32.7846 | −2.18080 | ||||||||
\(227\) | 10.3923 | 0.689761 | 0.344881 | − | 0.938647i | \(-0.387919\pi\) | ||||
0.344881 | + | 0.938647i | \(0.387919\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −18.5359 | −1.22489 | −0.612443 | − | 0.790515i | \(-0.709813\pi\) | ||||
−0.612443 | + | 0.790515i | \(0.709813\pi\) | |||||||
\(230\) | −6.00000 | −0.395628 | ||||||||
\(231\) | −12.9282 | −0.850613 | ||||||||
\(232\) | 14.1962 | 0.932023 | ||||||||
\(233\) | −7.85641 | −0.514690 | −0.257345 | − | 0.966320i | \(-0.582848\pi\) | ||||
−0.257345 | + | 0.966320i | \(0.582848\pi\) | |||||||
\(234\) | −1.26795 | −0.0828884 | ||||||||
\(235\) | −3.46410 | −0.225973 | ||||||||
\(236\) | 2.53590 | 0.165073 | ||||||||
\(237\) | −10.9282 | −0.709863 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.80385 | −0.634158 | −0.317079 | − | 0.948399i | \(-0.602702\pi\) | ||||
−0.317079 | + | 0.948399i | \(0.602702\pi\) | |||||||
\(240\) | −5.00000 | −0.322749 | ||||||||
\(241\) | −3.07180 | −0.197872 | −0.0989359 | − | 0.995094i | \(-0.531544\pi\) | ||||
−0.0989359 | + | 0.995094i | \(0.531544\pi\) | |||||||
\(242\) | −19.7321 | −1.26842 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −6.53590 | −0.418418 | ||||||||
\(245\) | 0.464102 | 0.0296504 | ||||||||
\(246\) | −2.19615 | −0.140022 | ||||||||
\(247\) | 0.732051 | 0.0465793 | ||||||||
\(248\) | 15.4641 | 0.981971 | ||||||||
\(249\) | −12.9282 | −0.819292 | ||||||||
\(250\) | −1.73205 | −0.109545 | ||||||||
\(251\) | 28.0526 | 1.77066 | 0.885331 | − | 0.464961i | \(-0.153932\pi\) | ||||
0.885331 | + | 0.464961i | \(0.153932\pi\) | |||||||
\(252\) | −2.73205 | −0.172103 | ||||||||
\(253\) | 16.3923 | 1.03058 | ||||||||
\(254\) | 6.92820 | 0.434714 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −24.0000 | −1.49708 | −0.748539 | − | 0.663090i | \(-0.769245\pi\) | ||||
−0.748539 | + | 0.663090i | \(0.769245\pi\) | |||||||
\(258\) | −7.26795 | −0.452483 | ||||||||
\(259\) | 16.9282 | 1.05187 | ||||||||
\(260\) | 0.732051 | 0.0453999 | ||||||||
\(261\) | 8.19615 | 0.507329 | ||||||||
\(262\) | 15.8038 | 0.976365 | ||||||||
\(263\) | 6.00000 | 0.369976 | 0.184988 | − | 0.982741i | \(-0.440775\pi\) | ||||
0.184988 | + | 0.982741i | \(0.440775\pi\) | |||||||
\(264\) | 8.19615 | 0.504438 | ||||||||
\(265\) | −9.46410 | −0.581375 | ||||||||
\(266\) | 4.73205 | 0.290141 | ||||||||
\(267\) | 10.7321 | 0.656791 | ||||||||
\(268\) | 8.00000 | 0.488678 | ||||||||
\(269\) | 0.588457 | 0.0358789 | 0.0179394 | − | 0.999839i | \(-0.494289\pi\) | ||||
0.0179394 | + | 0.999839i | \(0.494289\pi\) | |||||||
\(270\) | −1.73205 | −0.105409 | ||||||||
\(271\) | 0.392305 | 0.0238308 | 0.0119154 | − | 0.999929i | \(-0.496207\pi\) | ||||
0.0119154 | + | 0.999929i | \(0.496207\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.00000 | −0.121046 | ||||||||
\(274\) | −34.3923 | −2.07772 | ||||||||
\(275\) | 4.73205 | 0.285353 | ||||||||
\(276\) | 3.46410 | 0.208514 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 14.5359 | 0.871805 | ||||||||
\(279\) | 8.92820 | 0.534518 | ||||||||
\(280\) | −4.73205 | −0.282794 | ||||||||
\(281\) | 1.26795 | 0.0756395 | 0.0378198 | − | 0.999285i | \(-0.487959\pi\) | ||||
0.0378198 | + | 0.999285i | \(0.487959\pi\) | |||||||
\(282\) | 6.00000 | 0.357295 | ||||||||
\(283\) | 24.9808 | 1.48495 | 0.742476 | − | 0.669873i | \(-0.233651\pi\) | ||||
0.742476 | + | 0.669873i | \(0.233651\pi\) | |||||||
\(284\) | −4.39230 | −0.260635 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | −3.46410 | −0.204479 | ||||||||
\(288\) | 5.19615 | 0.306186 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | −14.1962 | −0.833627 | ||||||||
\(291\) | −6.19615 | −0.363225 | ||||||||
\(292\) | −16.9282 | −0.990648 | ||||||||
\(293\) | 27.7128 | 1.61900 | 0.809500 | − | 0.587120i | \(-0.199738\pi\) | ||||
0.809500 | + | 0.587120i | \(0.199738\pi\) | |||||||
\(294\) | −0.803848 | −0.0468813 | ||||||||
\(295\) | 2.53590 | 0.147646 | ||||||||
\(296\) | −10.7321 | −0.623788 | ||||||||
\(297\) | 4.73205 | 0.274581 | ||||||||
\(298\) | 34.3923 | 1.99229 | ||||||||
\(299\) | 2.53590 | 0.146655 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −11.4641 | −0.660780 | ||||||||
\(302\) | −24.2487 | −1.39536 | ||||||||
\(303\) | −10.3923 | −0.597022 | ||||||||
\(304\) | −5.00000 | −0.286770 | ||||||||
\(305\) | −6.53590 | −0.374244 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.3923 | −1.84873 | −0.924363 | − | 0.381514i | \(-0.875403\pi\) | ||||
−0.924363 | + | 0.381514i | \(0.875403\pi\) | |||||||
\(308\) | −12.9282 | −0.736653 | ||||||||
\(309\) | 9.85641 | 0.560711 | ||||||||
\(310\) | −15.4641 | −0.878302 | ||||||||
\(311\) | 32.4449 | 1.83978 | 0.919890 | − | 0.392177i | \(-0.128278\pi\) | ||||
0.919890 | + | 0.392177i | \(0.128278\pi\) | |||||||
\(312\) | 1.26795 | 0.0717835 | ||||||||
\(313\) | 6.39230 | 0.361314 | 0.180657 | − | 0.983546i | \(-0.442178\pi\) | ||||
0.180657 | + | 0.983546i | \(0.442178\pi\) | |||||||
\(314\) | −11.0718 | −0.624818 | ||||||||
\(315\) | −2.73205 | −0.153934 | ||||||||
\(316\) | −10.9282 | −0.614759 | ||||||||
\(317\) | −11.3205 | −0.635823 | −0.317912 | − | 0.948120i | \(-0.602982\pi\) | ||||
−0.317912 | + | 0.948120i | \(0.602982\pi\) | |||||||
\(318\) | 16.3923 | 0.919235 | ||||||||
\(319\) | 38.7846 | 2.17152 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 16.3923 | 0.913507 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.732051 | 0.0406069 | ||||||||
\(326\) | −16.0526 | −0.889069 | ||||||||
\(327\) | −14.3923 | −0.795896 | ||||||||
\(328\) | 2.19615 | 0.121262 | ||||||||
\(329\) | 9.46410 | 0.521773 | ||||||||
\(330\) | −8.19615 | −0.451183 | ||||||||
\(331\) | −25.7128 | −1.41330 | −0.706652 | − | 0.707561i | \(-0.749795\pi\) | ||||
−0.706652 | + | 0.707561i | \(0.749795\pi\) | |||||||
\(332\) | −12.9282 | −0.709527 | ||||||||
\(333\) | −6.19615 | −0.339547 | ||||||||
\(334\) | −6.00000 | −0.328305 | ||||||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 13.6603 | 0.745228 | ||||||||
\(337\) | 5.12436 | 0.279141 | 0.139571 | − | 0.990212i | \(-0.455428\pi\) | ||||
0.139571 | + | 0.990212i | \(0.455428\pi\) | |||||||
\(338\) | 21.5885 | 1.17426 | ||||||||
\(339\) | 18.9282 | 1.02804 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 42.2487 | 2.28790 | ||||||||
\(342\) | −1.73205 | −0.0936586 | ||||||||
\(343\) | 17.8564 | 0.964155 | ||||||||
\(344\) | 7.26795 | 0.391862 | ||||||||
\(345\) | 3.46410 | 0.186501 | ||||||||
\(346\) | −12.0000 | −0.645124 | ||||||||
\(347\) | −0.928203 | −0.0498286 | −0.0249143 | − | 0.999690i | \(-0.507931\pi\) | ||||
−0.0249143 | + | 0.999690i | \(0.507931\pi\) | |||||||
\(348\) | 8.19615 | 0.439360 | ||||||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 4.73205 | 0.252939 | ||||||||
\(351\) | 0.732051 | 0.0390740 | ||||||||
\(352\) | 24.5885 | 1.31057 | ||||||||
\(353\) | −14.7846 | −0.786905 | −0.393453 | − | 0.919345i | \(-0.628719\pi\) | ||||
−0.393453 | + | 0.919345i | \(0.628719\pi\) | |||||||
\(354\) | −4.39230 | −0.233448 | ||||||||
\(355\) | −4.39230 | −0.233119 | ||||||||
\(356\) | 10.7321 | 0.568798 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −40.3923 | −2.13480 | ||||||||
\(359\) | 0.339746 | 0.0179311 | 0.00896555 | − | 0.999960i | \(-0.497146\pi\) | ||||
0.00896555 | + | 0.999960i | \(0.497146\pi\) | |||||||
\(360\) | 1.73205 | 0.0912871 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 4.14359 | 0.217782 | ||||||||
\(363\) | 11.3923 | 0.597941 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | −16.9282 | −0.886063 | ||||||||
\(366\) | 11.3205 | 0.591732 | ||||||||
\(367\) | 16.1962 | 0.845432 | 0.422716 | − | 0.906262i | \(-0.361077\pi\) | ||||
0.422716 | + | 0.906262i | \(0.361077\pi\) | |||||||
\(368\) | −17.3205 | −0.902894 | ||||||||
\(369\) | 1.26795 | 0.0660068 | ||||||||
\(370\) | 10.7321 | 0.557933 | ||||||||
\(371\) | 25.8564 | 1.34240 | ||||||||
\(372\) | 8.92820 | 0.462906 | ||||||||
\(373\) | −6.19615 | −0.320825 | −0.160412 | − | 0.987050i | \(-0.551282\pi\) | ||||
−0.160412 | + | 0.987050i | \(0.551282\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −6.00000 | −0.309426 | ||||||||
\(377\) | 6.00000 | 0.309016 | ||||||||
\(378\) | 4.73205 | 0.243390 | ||||||||
\(379\) | 20.9282 | 1.07501 | 0.537505 | − | 0.843261i | \(-0.319367\pi\) | ||||
0.537505 | + | 0.843261i | \(0.319367\pi\) | |||||||
\(380\) | 1.00000 | 0.0512989 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | −0.588457 | −0.0301081 | ||||||||
\(383\) | −17.0718 | −0.872328 | −0.436164 | − | 0.899867i | \(-0.643663\pi\) | ||||
−0.436164 | + | 0.899867i | \(0.643663\pi\) | |||||||
\(384\) | −12.1244 | −0.618718 | ||||||||
\(385\) | −12.9282 | −0.658882 | ||||||||
\(386\) | −29.6603 | −1.50967 | ||||||||
\(387\) | 4.19615 | 0.213302 | ||||||||
\(388\) | −6.19615 | −0.314562 | ||||||||
\(389\) | 7.85641 | 0.398336 | 0.199168 | − | 0.979965i | \(-0.436176\pi\) | ||||
0.199168 | + | 0.979965i | \(0.436176\pi\) | |||||||
\(390\) | −1.26795 | −0.0642051 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.803848 | 0.0406004 | ||||||||
\(393\) | −9.12436 | −0.460263 | ||||||||
\(394\) | 41.5692 | 2.09423 | ||||||||
\(395\) | −10.9282 | −0.549858 | ||||||||
\(396\) | 4.73205 | 0.237795 | ||||||||
\(397\) | 8.92820 | 0.448094 | 0.224047 | − | 0.974578i | \(-0.428073\pi\) | ||||
0.224047 | + | 0.974578i | \(0.428073\pi\) | |||||||
\(398\) | 26.5359 | 1.33012 | ||||||||
\(399\) | −2.73205 | −0.136774 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −34.0526 | −1.70050 | −0.850252 | − | 0.526376i | \(-0.823550\pi\) | ||||
−0.850252 | + | 0.526376i | \(0.823550\pi\) | |||||||
\(402\) | −13.8564 | −0.691095 | ||||||||
\(403\) | 6.53590 | 0.325576 | ||||||||
\(404\) | −10.3923 | −0.517036 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 38.7846 | 1.92485 | ||||||||
\(407\) | −29.3205 | −1.45336 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.3923 | −1.30502 | −0.652508 | − | 0.757782i | \(-0.726283\pi\) | ||||
−0.652508 | + | 0.757782i | \(0.726283\pi\) | |||||||
\(410\) | −2.19615 | −0.108460 | ||||||||
\(411\) | 19.8564 | 0.979444 | ||||||||
\(412\) | 9.85641 | 0.485590 | ||||||||
\(413\) | −6.92820 | −0.340915 | ||||||||
\(414\) | −6.00000 | −0.294884 | ||||||||
\(415\) | −12.9282 | −0.634621 | ||||||||
\(416\) | 3.80385 | 0.186499 | ||||||||
\(417\) | −8.39230 | −0.410973 | ||||||||
\(418\) | −8.19615 | −0.400887 | ||||||||
\(419\) | −28.0526 | −1.37046 | −0.685229 | − | 0.728328i | \(-0.740298\pi\) | ||||
−0.685229 | + | 0.728328i | \(0.740298\pi\) | |||||||
\(420\) | −2.73205 | −0.133310 | ||||||||
\(421\) | −18.7846 | −0.915506 | −0.457753 | − | 0.889079i | \(-0.651346\pi\) | ||||
−0.457753 | + | 0.889079i | \(0.651346\pi\) | |||||||
\(422\) | −1.85641 | −0.0903685 | ||||||||
\(423\) | −3.46410 | −0.168430 | ||||||||
\(424\) | −16.3923 | −0.796081 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.60770 | 0.368594 | ||||||||
\(427\) | 17.8564 | 0.864132 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.46410 | 0.167248 | ||||||||
\(430\) | −7.26795 | −0.350492 | ||||||||
\(431\) | −11.3205 | −0.545290 | −0.272645 | − | 0.962115i | \(-0.587898\pi\) | ||||
−0.272645 | + | 0.962115i | \(0.587898\pi\) | |||||||
\(432\) | −5.00000 | −0.240563 | ||||||||
\(433\) | −10.5885 | −0.508849 | −0.254424 | − | 0.967093i | \(-0.581886\pi\) | ||||
−0.254424 | + | 0.967093i | \(0.581886\pi\) | |||||||
\(434\) | 42.2487 | 2.02800 | ||||||||
\(435\) | 8.19615 | 0.392975 | ||||||||
\(436\) | −14.3923 | −0.689266 | ||||||||
\(437\) | 3.46410 | 0.165710 | ||||||||
\(438\) | 29.3205 | 1.40099 | ||||||||
\(439\) | 26.9282 | 1.28521 | 0.642607 | − | 0.766196i | \(-0.277853\pi\) | ||||
0.642607 | + | 0.766196i | \(0.277853\pi\) | |||||||
\(440\) | 8.19615 | 0.390736 | ||||||||
\(441\) | 0.464102 | 0.0221001 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.32051 | −0.252785 | −0.126392 | − | 0.991980i | \(-0.540340\pi\) | ||||
−0.126392 | + | 0.991980i | \(0.540340\pi\) | |||||||
\(444\) | −6.19615 | −0.294056 | ||||||||
\(445\) | 10.7321 | 0.508748 | ||||||||
\(446\) | 30.9282 | 1.46449 | ||||||||
\(447\) | −19.8564 | −0.939176 | ||||||||
\(448\) | −2.73205 | −0.129077 | ||||||||
\(449\) | −5.66025 | −0.267124 | −0.133562 | − | 0.991040i | \(-0.542642\pi\) | ||||
−0.133562 | + | 0.991040i | \(0.542642\pi\) | |||||||
\(450\) | −1.73205 | −0.0816497 | ||||||||
\(451\) | 6.00000 | 0.282529 | ||||||||
\(452\) | 18.9282 | 0.890308 | ||||||||
\(453\) | 14.0000 | 0.657777 | ||||||||
\(454\) | −18.0000 | −0.844782 | ||||||||
\(455\) | −2.00000 | −0.0937614 | ||||||||
\(456\) | 1.73205 | 0.0811107 | ||||||||
\(457\) | 4.53590 | 0.212180 | 0.106090 | − | 0.994357i | \(-0.466167\pi\) | ||||
0.106090 | + | 0.994357i | \(0.466167\pi\) | |||||||
\(458\) | 32.1051 | 1.50017 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.46410 | 0.161515 | ||||||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | 22.3923 | 1.04178 | ||||||||
\(463\) | −35.5167 | −1.65060 | −0.825300 | − | 0.564695i | \(-0.808994\pi\) | ||||
−0.825300 | + | 0.564695i | \(0.808994\pi\) | |||||||
\(464\) | −40.9808 | −1.90248 | ||||||||
\(465\) | 8.92820 | 0.414036 | ||||||||
\(466\) | 13.6077 | 0.630364 | ||||||||
\(467\) | 20.5359 | 0.950288 | 0.475144 | − | 0.879908i | \(-0.342396\pi\) | ||||
0.475144 | + | 0.879908i | \(0.342396\pi\) | |||||||
\(468\) | 0.732051 | 0.0338391 | ||||||||
\(469\) | −21.8564 | −1.00924 | ||||||||
\(470\) | 6.00000 | 0.276759 | ||||||||
\(471\) | 6.39230 | 0.294542 | ||||||||
\(472\) | 4.39230 | 0.202172 | ||||||||
\(473\) | 19.8564 | 0.912999 | ||||||||
\(474\) | 18.9282 | 0.869401 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.46410 | −0.433331 | ||||||||
\(478\) | 16.9808 | 0.776682 | ||||||||
\(479\) | 25.5167 | 1.16589 | 0.582943 | − | 0.812513i | \(-0.301901\pi\) | ||||
0.582943 | + | 0.812513i | \(0.301901\pi\) | |||||||
\(480\) | 5.19615 | 0.237171 | ||||||||
\(481\) | −4.53590 | −0.206819 | ||||||||
\(482\) | 5.32051 | 0.242343 | ||||||||
\(483\) | −9.46410 | −0.430632 | ||||||||
\(484\) | 11.3923 | 0.517832 | ||||||||
\(485\) | −6.19615 | −0.281353 | ||||||||
\(486\) | −1.73205 | −0.0785674 | ||||||||
\(487\) | −32.3923 | −1.46784 | −0.733918 | − | 0.679238i | \(-0.762310\pi\) | ||||
−0.733918 | + | 0.679238i | \(0.762310\pi\) | |||||||
\(488\) | −11.3205 | −0.512455 | ||||||||
\(489\) | 9.26795 | 0.419111 | ||||||||
\(490\) | −0.803848 | −0.0363141 | ||||||||
\(491\) | 16.0526 | 0.724442 | 0.362221 | − | 0.932092i | \(-0.382019\pi\) | ||||
0.362221 | + | 0.932092i | \(0.382019\pi\) | |||||||
\(492\) | 1.26795 | 0.0571636 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −1.26795 | −0.0570477 | ||||||||
\(495\) | 4.73205 | 0.212690 | ||||||||
\(496\) | −44.6410 | −2.00444 | ||||||||
\(497\) | 12.0000 | 0.538274 | ||||||||
\(498\) | 22.3923 | 1.00342 | ||||||||
\(499\) | 10.5359 | 0.471652 | 0.235826 | − | 0.971795i | \(-0.424221\pi\) | ||||
0.235826 | + | 0.971795i | \(0.424221\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 3.46410 | 0.154765 | ||||||||
\(502\) | −48.5885 | −2.16861 | ||||||||
\(503\) | −23.0718 | −1.02872 | −0.514360 | − | 0.857574i | \(-0.671971\pi\) | ||||
−0.514360 | + | 0.857574i | \(0.671971\pi\) | |||||||
\(504\) | −4.73205 | −0.210782 | ||||||||
\(505\) | −10.3923 | −0.462451 | ||||||||
\(506\) | −28.3923 | −1.26219 | ||||||||
\(507\) | −12.4641 | −0.553550 | ||||||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | −10.0526 | −0.445572 | −0.222786 | − | 0.974867i | \(-0.571515\pi\) | ||||
−0.222786 | + | 0.974867i | \(0.571515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 46.2487 | 2.04592 | ||||||||
\(512\) | −8.66025 | −0.382733 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 41.5692 | 1.83354 | ||||||||
\(515\) | 9.85641 | 0.434325 | ||||||||
\(516\) | 4.19615 | 0.184725 | ||||||||
\(517\) | −16.3923 | −0.720933 | ||||||||
\(518\) | −29.3205 | −1.28827 | ||||||||
\(519\) | 6.92820 | 0.304114 | ||||||||
\(520\) | 1.26795 | 0.0556033 | ||||||||
\(521\) | 37.2679 | 1.63274 | 0.816369 | − | 0.577530i | \(-0.195983\pi\) | ||||
0.816369 | + | 0.577530i | \(0.195983\pi\) | |||||||
\(522\) | −14.1962 | −0.621349 | ||||||||
\(523\) | 8.67949 | 0.379528 | 0.189764 | − | 0.981830i | \(-0.439228\pi\) | ||||
0.189764 | + | 0.981830i | \(0.439228\pi\) | |||||||
\(524\) | −9.12436 | −0.398599 | ||||||||
\(525\) | −2.73205 | −0.119236 | ||||||||
\(526\) | −10.3923 | −0.453126 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −23.6603 | −1.02968 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 16.3923 | 0.712036 | ||||||||
\(531\) | 2.53590 | 0.110049 | ||||||||
\(532\) | −2.73205 | −0.118449 | ||||||||
\(533\) | 0.928203 | 0.0402049 | ||||||||
\(534\) | −18.5885 | −0.804401 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13.8564 | 0.598506 | ||||||||
\(537\) | 23.3205 | 1.00635 | ||||||||
\(538\) | −1.01924 | −0.0439425 | ||||||||
\(539\) | 2.19615 | 0.0945950 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 41.7128 | 1.79337 | 0.896687 | − | 0.442665i | \(-0.145967\pi\) | ||||
0.896687 | + | 0.442665i | \(0.145967\pi\) | |||||||
\(542\) | −0.679492 | −0.0291867 | ||||||||
\(543\) | −2.39230 | −0.102664 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.3923 | −0.616499 | ||||||||
\(546\) | 3.46410 | 0.148250 | ||||||||
\(547\) | 43.3205 | 1.85225 | 0.926126 | − | 0.377215i | \(-0.123118\pi\) | ||||
0.926126 | + | 0.377215i | \(0.123118\pi\) | |||||||
\(548\) | 19.8564 | 0.848224 | ||||||||
\(549\) | −6.53590 | −0.278945 | ||||||||
\(550\) | −8.19615 | −0.349485 | ||||||||
\(551\) | 8.19615 | 0.349168 | ||||||||
\(552\) | 6.00000 | 0.255377 | ||||||||
\(553\) | 29.8564 | 1.26962 | ||||||||
\(554\) | −3.46410 | −0.147176 | ||||||||
\(555\) | −6.19615 | −0.263012 | ||||||||
\(556\) | −8.39230 | −0.355913 | ||||||||
\(557\) | 0.928203 | 0.0393292 | 0.0196646 | − | 0.999807i | \(-0.493740\pi\) | ||||
0.0196646 | + | 0.999807i | \(0.493740\pi\) | |||||||
\(558\) | −15.4641 | −0.654648 | ||||||||
\(559\) | 3.07180 | 0.129923 | ||||||||
\(560\) | 13.6603 | 0.577251 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.19615 | −0.0926391 | ||||||||
\(563\) | −27.4641 | −1.15747 | −0.578737 | − | 0.815514i | \(-0.696454\pi\) | ||||
−0.578737 | + | 0.815514i | \(0.696454\pi\) | |||||||
\(564\) | −3.46410 | −0.145865 | ||||||||
\(565\) | 18.9282 | 0.796315 | ||||||||
\(566\) | −43.2679 | −1.81869 | ||||||||
\(567\) | −2.73205 | −0.114735 | ||||||||
\(568\) | −7.60770 | −0.319212 | ||||||||
\(569\) | 22.0526 | 0.924491 | 0.462246 | − | 0.886752i | \(-0.347044\pi\) | ||||
0.462246 | + | 0.886752i | \(0.347044\pi\) | |||||||
\(570\) | −1.73205 | −0.0725476 | ||||||||
\(571\) | −34.2487 | −1.43326 | −0.716632 | − | 0.697452i | \(-0.754317\pi\) | ||||
−0.716632 | + | 0.697452i | \(0.754317\pi\) | |||||||
\(572\) | 3.46410 | 0.144841 | ||||||||
\(573\) | 0.339746 | 0.0141931 | ||||||||
\(574\) | 6.00000 | 0.250435 | ||||||||
\(575\) | 3.46410 | 0.144463 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 15.1769 | 0.631823 | 0.315912 | − | 0.948789i | \(-0.397690\pi\) | ||||
0.315912 | + | 0.948789i | \(0.397690\pi\) | |||||||
\(578\) | 29.4449 | 1.22474 | ||||||||
\(579\) | 17.1244 | 0.711664 | ||||||||
\(580\) | 8.19615 | 0.340327 | ||||||||
\(581\) | 35.3205 | 1.46534 | ||||||||
\(582\) | 10.7321 | 0.444858 | ||||||||
\(583\) | −44.7846 | −1.85479 | ||||||||
\(584\) | −29.3205 | −1.21329 | ||||||||
\(585\) | 0.732051 | 0.0302666 | ||||||||
\(586\) | −48.0000 | −1.98286 | ||||||||
\(587\) | −3.46410 | −0.142979 | −0.0714894 | − | 0.997441i | \(-0.522775\pi\) | ||||
−0.0714894 | + | 0.997441i | \(0.522775\pi\) | |||||||
\(588\) | 0.464102 | 0.0191392 | ||||||||
\(589\) | 8.92820 | 0.367880 | ||||||||
\(590\) | −4.39230 | −0.180828 | ||||||||
\(591\) | −24.0000 | −0.987228 | ||||||||
\(592\) | 30.9808 | 1.27330 | ||||||||
\(593\) | −38.7846 | −1.59269 | −0.796347 | − | 0.604841i | \(-0.793237\pi\) | ||||
−0.796347 | + | 0.604841i | \(0.793237\pi\) | |||||||
\(594\) | −8.19615 | −0.336292 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.8564 | −0.813350 | ||||||||
\(597\) | −15.3205 | −0.627027 | ||||||||
\(598\) | −4.39230 | −0.179615 | ||||||||
\(599\) | −13.8564 | −0.566157 | −0.283079 | − | 0.959097i | \(-0.591356\pi\) | ||||
−0.283079 | + | 0.959097i | \(0.591356\pi\) | |||||||
\(600\) | 1.73205 | 0.0707107 | ||||||||
\(601\) | −47.1769 | −1.92439 | −0.962193 | − | 0.272368i | \(-0.912193\pi\) | ||||
−0.962193 | + | 0.272368i | \(0.912193\pi\) | |||||||
\(602\) | 19.8564 | 0.809287 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 14.0000 | 0.569652 | ||||||||
\(605\) | 11.3923 | 0.463163 | ||||||||
\(606\) | 18.0000 | 0.731200 | ||||||||
\(607\) | −11.6077 | −0.471142 | −0.235571 | − | 0.971857i | \(-0.575696\pi\) | ||||
−0.235571 | + | 0.971857i | \(0.575696\pi\) | |||||||
\(608\) | 5.19615 | 0.210732 | ||||||||
\(609\) | −22.3923 | −0.907382 | ||||||||
\(610\) | 11.3205 | 0.458354 | ||||||||
\(611\) | −2.53590 | −0.102591 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.3923 | 1.71221 | 0.856105 | − | 0.516803i | \(-0.172878\pi\) | ||||
0.856105 | + | 0.516803i | \(0.172878\pi\) | |||||||
\(614\) | 56.1051 | 2.26422 | ||||||||
\(615\) | 1.26795 | 0.0511286 | ||||||||
\(616\) | −22.3923 | −0.902212 | ||||||||
\(617\) | 27.7128 | 1.11568 | 0.557838 | − | 0.829950i | \(-0.311631\pi\) | ||||
0.557838 | + | 0.829950i | \(0.311631\pi\) | |||||||
\(618\) | −17.0718 | −0.686728 | ||||||||
\(619\) | −15.3205 | −0.615783 | −0.307892 | − | 0.951421i | \(-0.599623\pi\) | ||||
−0.307892 | + | 0.951421i | \(0.599623\pi\) | |||||||
\(620\) | 8.92820 | 0.358565 | ||||||||
\(621\) | 3.46410 | 0.139010 | ||||||||
\(622\) | −56.1962 | −2.25326 | ||||||||
\(623\) | −29.3205 | −1.17470 | ||||||||
\(624\) | −3.66025 | −0.146527 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −11.0718 | −0.442518 | ||||||||
\(627\) | 4.73205 | 0.188980 | ||||||||
\(628\) | 6.39230 | 0.255081 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 4.73205 | 0.188529 | ||||||||
\(631\) | −34.9282 | −1.39047 | −0.695235 | − | 0.718783i | \(-0.744700\pi\) | ||||
−0.695235 | + | 0.718783i | \(0.744700\pi\) | |||||||
\(632\) | −18.9282 | −0.752923 | ||||||||
\(633\) | 1.07180 | 0.0426001 | ||||||||
\(634\) | 19.6077 | 0.778721 | ||||||||
\(635\) | −4.00000 | −0.158735 | ||||||||
\(636\) | −9.46410 | −0.375276 | ||||||||
\(637\) | 0.339746 | 0.0134612 | ||||||||
\(638\) | −67.1769 | −2.65956 | ||||||||
\(639\) | −4.39230 | −0.173757 | ||||||||
\(640\) | −12.1244 | −0.479257 | ||||||||
\(641\) | 48.5885 | 1.91913 | 0.959564 | − | 0.281489i | \(-0.0908284\pi\) | ||||
0.959564 | + | 0.281489i | \(0.0908284\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.1962 | −0.480969 | −0.240485 | − | 0.970653i | \(-0.577306\pi\) | ||||
−0.240485 | + | 0.970653i | \(0.577306\pi\) | |||||||
\(644\) | −9.46410 | −0.372938 | ||||||||
\(645\) | 4.19615 | 0.165223 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.14359 | −0.162901 | −0.0814507 | − | 0.996677i | \(-0.525955\pi\) | ||||
−0.0814507 | + | 0.996677i | \(0.525955\pi\) | |||||||
\(648\) | 1.73205 | 0.0680414 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | −1.26795 | −0.0497331 | ||||||||
\(651\) | −24.3923 | −0.956010 | ||||||||
\(652\) | 9.26795 | 0.362961 | ||||||||
\(653\) | 17.0718 | 0.668071 | 0.334036 | − | 0.942560i | \(-0.391589\pi\) | ||||
0.334036 | + | 0.942560i | \(0.391589\pi\) | |||||||
\(654\) | 24.9282 | 0.974770 | ||||||||
\(655\) | −9.12436 | −0.356518 | ||||||||
\(656\) | −6.33975 | −0.247525 | ||||||||
\(657\) | −16.9282 | −0.660432 | ||||||||
\(658\) | −16.3923 | −0.639039 | ||||||||
\(659\) | 5.07180 | 0.197569 | 0.0987846 | − | 0.995109i | \(-0.468505\pi\) | ||||
0.0987846 | + | 0.995109i | \(0.468505\pi\) | |||||||
\(660\) | 4.73205 | 0.184195 | ||||||||
\(661\) | 39.1769 | 1.52381 | 0.761903 | − | 0.647692i | \(-0.224265\pi\) | ||||
0.761903 | + | 0.647692i | \(0.224265\pi\) | |||||||
\(662\) | 44.5359 | 1.73094 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −22.3923 | −0.868990 | ||||||||
\(665\) | −2.73205 | −0.105944 | ||||||||
\(666\) | 10.7321 | 0.415859 | ||||||||
\(667\) | 28.3923 | 1.09935 | ||||||||
\(668\) | 3.46410 | 0.134030 | ||||||||
\(669\) | −17.8564 | −0.690369 | ||||||||
\(670\) | −13.8564 | −0.535320 | ||||||||
\(671\) | −30.9282 | −1.19397 | ||||||||
\(672\) | −14.1962 | −0.547628 | ||||||||
\(673\) | 17.1244 | 0.660095 | 0.330048 | − | 0.943964i | \(-0.392935\pi\) | ||||
0.330048 | + | 0.943964i | \(0.392935\pi\) | |||||||
\(674\) | −8.87564 | −0.341877 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −12.4641 | −0.479389 | ||||||||
\(677\) | 0.679492 | 0.0261150 | 0.0130575 | − | 0.999915i | \(-0.495844\pi\) | ||||
0.0130575 | + | 0.999915i | \(0.495844\pi\) | |||||||
\(678\) | −32.7846 | −1.25909 | ||||||||
\(679\) | 16.9282 | 0.649645 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.3923 | 0.398234 | ||||||||
\(682\) | −73.1769 | −2.80209 | ||||||||
\(683\) | −5.07180 | −0.194067 | −0.0970335 | − | 0.995281i | \(-0.530935\pi\) | ||||
−0.0970335 | + | 0.995281i | \(0.530935\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 19.8564 | 0.758674 | ||||||||
\(686\) | −30.9282 | −1.18084 | ||||||||
\(687\) | −18.5359 | −0.707189 | ||||||||
\(688\) | −20.9808 | −0.799884 | ||||||||
\(689\) | −6.92820 | −0.263944 | ||||||||
\(690\) | −6.00000 | −0.228416 | ||||||||
\(691\) | 12.3923 | 0.471425 | 0.235713 | − | 0.971823i | \(-0.424258\pi\) | ||||
0.235713 | + | 0.971823i | \(0.424258\pi\) | |||||||
\(692\) | 6.92820 | 0.263371 | ||||||||
\(693\) | −12.9282 | −0.491102 | ||||||||
\(694\) | 1.60770 | 0.0610273 | ||||||||
\(695\) | −8.39230 | −0.318338 | ||||||||
\(696\) | 14.1962 | 0.538104 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 38.1051 | 1.44230 | ||||||||
\(699\) | −7.85641 | −0.297157 | ||||||||
\(700\) | −2.73205 | −0.103262 | ||||||||
\(701\) | −33.7128 | −1.27332 | −0.636658 | − | 0.771147i | \(-0.719684\pi\) | ||||
−0.636658 | + | 0.771147i | \(0.719684\pi\) | |||||||
\(702\) | −1.26795 | −0.0478557 | ||||||||
\(703\) | −6.19615 | −0.233692 | ||||||||
\(704\) | 4.73205 | 0.178346 | ||||||||
\(705\) | −3.46410 | −0.130466 | ||||||||
\(706\) | 25.6077 | 0.963758 | ||||||||
\(707\) | 28.3923 | 1.06780 | ||||||||
\(708\) | 2.53590 | 0.0953049 | ||||||||
\(709\) | −29.1769 | −1.09576 | −0.547881 | − | 0.836556i | \(-0.684565\pi\) | ||||
−0.547881 | + | 0.836556i | \(0.684565\pi\) | |||||||
\(710\) | 7.60770 | 0.285512 | ||||||||
\(711\) | −10.9282 | −0.409840 | ||||||||
\(712\) | 18.5885 | 0.696632 | ||||||||
\(713\) | 30.9282 | 1.15827 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.46410 | 0.129550 | ||||||||
\(716\) | 23.3205 | 0.871528 | ||||||||
\(717\) | −9.80385 | −0.366131 | ||||||||
\(718\) | −0.588457 | −0.0219610 | ||||||||
\(719\) | −11.6603 | −0.434854 | −0.217427 | − | 0.976077i | \(-0.569766\pi\) | ||||
−0.217427 | + | 0.976077i | \(0.569766\pi\) | |||||||
\(720\) | −5.00000 | −0.186339 | ||||||||
\(721\) | −26.9282 | −1.00286 | ||||||||
\(722\) | −1.73205 | −0.0644603 | ||||||||
\(723\) | −3.07180 | −0.114241 | ||||||||
\(724\) | −2.39230 | −0.0889093 | ||||||||
\(725\) | 8.19615 | 0.304397 | ||||||||
\(726\) | −19.7321 | −0.732325 | ||||||||
\(727\) | 25.6603 | 0.951686 | 0.475843 | − | 0.879530i | \(-0.342143\pi\) | ||||
0.475843 | + | 0.879530i | \(0.342143\pi\) | |||||||
\(728\) | −3.46410 | −0.128388 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 29.3205 | 1.08520 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −6.53590 | −0.241574 | ||||||||
\(733\) | −18.7846 | −0.693825 | −0.346913 | − | 0.937897i | \(-0.612770\pi\) | ||||
−0.346913 | + | 0.937897i | \(0.612770\pi\) | |||||||
\(734\) | −28.0526 | −1.03544 | ||||||||
\(735\) | 0.464102 | 0.0171186 | ||||||||
\(736\) | 18.0000 | 0.663489 | ||||||||
\(737\) | 37.8564 | 1.39446 | ||||||||
\(738\) | −2.19615 | −0.0808415 | ||||||||
\(739\) | 6.14359 | 0.225996 | 0.112998 | − | 0.993595i | \(-0.463955\pi\) | ||||
0.112998 | + | 0.993595i | \(0.463955\pi\) | |||||||
\(740\) | −6.19615 | −0.227775 | ||||||||
\(741\) | 0.732051 | 0.0268926 | ||||||||
\(742\) | −44.7846 | −1.64409 | ||||||||
\(743\) | −3.21539 | −0.117961 | −0.0589806 | − | 0.998259i | \(-0.518785\pi\) | ||||
−0.0589806 | + | 0.998259i | \(0.518785\pi\) | |||||||
\(744\) | 15.4641 | 0.566941 | ||||||||
\(745\) | −19.8564 | −0.727482 | ||||||||
\(746\) | 10.7321 | 0.392928 | ||||||||
\(747\) | −12.9282 | −0.473018 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.73205 | −0.0632456 | ||||||||
\(751\) | 26.0000 | 0.948753 | 0.474377 | − | 0.880322i | \(-0.342673\pi\) | ||||
0.474377 | + | 0.880322i | \(0.342673\pi\) | |||||||
\(752\) | 17.3205 | 0.631614 | ||||||||
\(753\) | 28.0526 | 1.02229 | ||||||||
\(754\) | −10.3923 | −0.378465 | ||||||||
\(755\) | 14.0000 | 0.509512 | ||||||||
\(756\) | −2.73205 | −0.0993637 | ||||||||
\(757\) | 32.2487 | 1.17210 | 0.586050 | − | 0.810275i | \(-0.300682\pi\) | ||||
0.586050 | + | 0.810275i | \(0.300682\pi\) | |||||||
\(758\) | −36.2487 | −1.31661 | ||||||||
\(759\) | 16.3923 | 0.595003 | ||||||||
\(760\) | 1.73205 | 0.0628281 | ||||||||
\(761\) | 6.00000 | 0.217500 | 0.108750 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108750 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(762\) | 6.92820 | 0.250982 | ||||||||
\(763\) | 39.3205 | 1.42350 | ||||||||
\(764\) | 0.339746 | 0.0122916 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.5692 | 1.06838 | ||||||||
\(767\) | 1.85641 | 0.0670310 | ||||||||
\(768\) | 19.0000 | 0.685603 | ||||||||
\(769\) | −20.6410 | −0.744334 | −0.372167 | − | 0.928166i | \(-0.621385\pi\) | ||||
−0.372167 | + | 0.928166i | \(0.621385\pi\) | |||||||
\(770\) | 22.3923 | 0.806963 | ||||||||
\(771\) | −24.0000 | −0.864339 | ||||||||
\(772\) | 17.1244 | 0.616319 | ||||||||
\(773\) | −25.1769 | −0.905551 | −0.452775 | − | 0.891625i | \(-0.649566\pi\) | ||||
−0.452775 | + | 0.891625i | \(0.649566\pi\) | |||||||
\(774\) | −7.26795 | −0.261241 | ||||||||
\(775\) | 8.92820 | 0.320711 | ||||||||
\(776\) | −10.7321 | −0.385258 | ||||||||
\(777\) | 16.9282 | 0.607296 | ||||||||
\(778\) | −13.6077 | −0.487860 | ||||||||
\(779\) | 1.26795 | 0.0454290 | ||||||||
\(780\) | 0.732051 | 0.0262116 | ||||||||
\(781\) | −20.7846 | −0.743732 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.19615 | 0.292907 | ||||||||
\(784\) | −2.32051 | −0.0828753 | ||||||||
\(785\) | 6.39230 | 0.228151 | ||||||||
\(786\) | 15.8038 | 0.563705 | ||||||||
\(787\) | 8.67949 | 0.309390 | 0.154695 | − | 0.987962i | \(-0.450560\pi\) | ||||
0.154695 | + | 0.987962i | \(0.450560\pi\) | |||||||
\(788\) | −24.0000 | −0.854965 | ||||||||
\(789\) | 6.00000 | 0.213606 | ||||||||
\(790\) | 18.9282 | 0.673435 | ||||||||
\(791\) | −51.7128 | −1.83870 | ||||||||
\(792\) | 8.19615 | 0.291238 | ||||||||
\(793\) | −4.78461 | −0.169906 | ||||||||
\(794\) | −15.4641 | −0.548800 | ||||||||
\(795\) | −9.46410 | −0.335657 | ||||||||
\(796\) | −15.3205 | −0.543021 | ||||||||
\(797\) | 44.7846 | 1.58635 | 0.793176 | − | 0.608992i | \(-0.208426\pi\) | ||||
0.793176 | + | 0.608992i | \(0.208426\pi\) | |||||||
\(798\) | 4.73205 | 0.167513 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 5.19615 | 0.183712 | ||||||||
\(801\) | 10.7321 | 0.379198 | ||||||||
\(802\) | 58.9808 | 2.08268 | ||||||||
\(803\) | −80.1051 | −2.82685 | ||||||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | −9.46410 | −0.333566 | ||||||||
\(806\) | −11.3205 | −0.398748 | ||||||||
\(807\) | 0.588457 | 0.0207147 | ||||||||
\(808\) | −18.0000 | −0.633238 | ||||||||
\(809\) | 14.7846 | 0.519799 | 0.259900 | − | 0.965636i | \(-0.416311\pi\) | ||||
0.259900 | + | 0.965636i | \(0.416311\pi\) | |||||||
\(810\) | −1.73205 | −0.0608581 | ||||||||
\(811\) | 37.5692 | 1.31923 | 0.659617 | − | 0.751602i | \(-0.270719\pi\) | ||||
0.659617 | + | 0.751602i | \(0.270719\pi\) | |||||||
\(812\) | −22.3923 | −0.785816 | ||||||||
\(813\) | 0.392305 | 0.0137587 | ||||||||
\(814\) | 50.7846 | 1.78000 | ||||||||
\(815\) | 9.26795 | 0.324642 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.19615 | 0.146805 | ||||||||
\(818\) | 45.7128 | 1.59831 | ||||||||
\(819\) | −2.00000 | −0.0698857 | ||||||||
\(820\) | 1.26795 | 0.0442787 | ||||||||
\(821\) | −32.5359 | −1.13551 | −0.567755 | − | 0.823197i | \(-0.692188\pi\) | ||||
−0.567755 | + | 0.823197i | \(0.692188\pi\) | |||||||
\(822\) | −34.3923 | −1.19957 | ||||||||
\(823\) | 12.9808 | 0.452481 | 0.226240 | − | 0.974071i | \(-0.427356\pi\) | ||||
0.226240 | + | 0.974071i | \(0.427356\pi\) | |||||||
\(824\) | 17.0718 | 0.594724 | ||||||||
\(825\) | 4.73205 | 0.164749 | ||||||||
\(826\) | 12.0000 | 0.417533 | ||||||||
\(827\) | −5.32051 | −0.185012 | −0.0925061 | − | 0.995712i | \(-0.529488\pi\) | ||||
−0.0925061 | + | 0.995712i | \(0.529488\pi\) | |||||||
\(828\) | 3.46410 | 0.120386 | ||||||||
\(829\) | 34.1051 | 1.18452 | 0.592260 | − | 0.805747i | \(-0.298236\pi\) | ||||
0.592260 | + | 0.805747i | \(0.298236\pi\) | |||||||
\(830\) | 22.3923 | 0.777248 | ||||||||
\(831\) | 2.00000 | 0.0693792 | ||||||||
\(832\) | 0.732051 | 0.0253793 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.5359 | 0.503337 | ||||||||
\(835\) | 3.46410 | 0.119880 | ||||||||
\(836\) | 4.73205 | 0.163661 | ||||||||
\(837\) | 8.92820 | 0.308604 | ||||||||
\(838\) | 48.5885 | 1.67846 | ||||||||
\(839\) | −19.6077 | −0.676933 | −0.338466 | − | 0.940978i | \(-0.609908\pi\) | ||||
−0.338466 | + | 0.940978i | \(0.609908\pi\) | |||||||
\(840\) | −4.73205 | −0.163271 | ||||||||
\(841\) | 38.1769 | 1.31645 | ||||||||
\(842\) | 32.5359 | 1.12126 | ||||||||
\(843\) | 1.26795 | 0.0436705 | ||||||||
\(844\) | 1.07180 | 0.0368928 | ||||||||
\(845\) | −12.4641 | −0.428778 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | −31.1244 | −1.06945 | ||||||||
\(848\) | 47.3205 | 1.62499 | ||||||||
\(849\) | 24.9808 | 0.857338 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.4641 | −0.735780 | ||||||||
\(852\) | −4.39230 | −0.150478 | ||||||||
\(853\) | 27.1769 | 0.930520 | 0.465260 | − | 0.885174i | \(-0.345961\pi\) | ||||
0.465260 | + | 0.885174i | \(0.345961\pi\) | |||||||
\(854\) | −30.9282 | −1.05834 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.2487 | −1.44319 | −0.721594 | − | 0.692316i | \(-0.756590\pi\) | ||||
−0.721594 | + | 0.692316i | \(0.756590\pi\) | |||||||
\(858\) | −6.00000 | −0.204837 | ||||||||
\(859\) | 32.0000 | 1.09183 | 0.545913 | − | 0.837842i | \(-0.316183\pi\) | ||||
0.545913 | + | 0.837842i | \(0.316183\pi\) | |||||||
\(860\) | 4.19615 | 0.143088 | ||||||||
\(861\) | −3.46410 | −0.118056 | ||||||||
\(862\) | 19.6077 | 0.667841 | ||||||||
\(863\) | −12.0000 | −0.408485 | −0.204242 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(864\) | 5.19615 | 0.176777 | ||||||||
\(865\) | 6.92820 | 0.235566 | ||||||||
\(866\) | 18.3397 | 0.623210 | ||||||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | −24.3923 | −0.827929 | ||||||||
\(869\) | −51.7128 | −1.75424 | ||||||||
\(870\) | −14.1962 | −0.481295 | ||||||||
\(871\) | 5.85641 | 0.198437 | ||||||||
\(872\) | −24.9282 | −0.844175 | ||||||||
\(873\) | −6.19615 | −0.209708 | ||||||||
\(874\) | −6.00000 | −0.202953 | ||||||||
\(875\) | −2.73205 | −0.0923602 | ||||||||
\(876\) | −16.9282 | −0.571951 | ||||||||
\(877\) | 53.1244 | 1.79388 | 0.896941 | − | 0.442150i | \(-0.145784\pi\) | ||||
0.896941 | + | 0.442150i | \(0.145784\pi\) | |||||||
\(878\) | −46.6410 | −1.57406 | ||||||||
\(879\) | 27.7128 | 0.934730 | ||||||||
\(880\) | −23.6603 | −0.797587 | ||||||||
\(881\) | 8.53590 | 0.287582 | 0.143791 | − | 0.989608i | \(-0.454071\pi\) | ||||
0.143791 | + | 0.989608i | \(0.454071\pi\) | |||||||
\(882\) | −0.803848 | −0.0270670 | ||||||||
\(883\) | 36.9808 | 1.24450 | 0.622251 | − | 0.782818i | \(-0.286218\pi\) | ||||
0.622251 | + | 0.782818i | \(0.286218\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.53590 | 0.0852433 | ||||||||
\(886\) | 9.21539 | 0.309597 | ||||||||
\(887\) | −24.0000 | −0.805841 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(888\) | −10.7321 | −0.360144 | ||||||||
\(889\) | 10.9282 | 0.366520 | ||||||||
\(890\) | −18.5885 | −0.623087 | ||||||||
\(891\) | 4.73205 | 0.158530 | ||||||||
\(892\) | −17.8564 | −0.597877 | ||||||||
\(893\) | −3.46410 | −0.115922 | ||||||||
\(894\) | 34.3923 | 1.15025 | ||||||||
\(895\) | 23.3205 | 0.779519 | ||||||||
\(896\) | 33.1244 | 1.10661 | ||||||||
\(897\) | 2.53590 | 0.0846712 | ||||||||
\(898\) | 9.80385 | 0.327159 | ||||||||
\(899\) | 73.1769 | 2.44059 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −10.3923 | −0.346026 | ||||||||
\(903\) | −11.4641 | −0.381501 | ||||||||
\(904\) | 32.7846 | 1.09040 | ||||||||
\(905\) | −2.39230 | −0.0795229 | ||||||||
\(906\) | −24.2487 | −0.805609 | ||||||||
\(907\) | −32.3923 | −1.07557 | −0.537784 | − | 0.843082i | \(-0.680739\pi\) | ||||
−0.537784 | + | 0.843082i | \(0.680739\pi\) | |||||||
\(908\) | 10.3923 | 0.344881 | ||||||||
\(909\) | −10.3923 | −0.344691 | ||||||||
\(910\) | 3.46410 | 0.114834 | ||||||||
\(911\) | −54.9282 | −1.81985 | −0.909926 | − | 0.414770i | \(-0.863862\pi\) | ||||
−0.909926 | + | 0.414770i | \(0.863862\pi\) | |||||||
\(912\) | −5.00000 | −0.165567 | ||||||||
\(913\) | −61.1769 | −2.02466 | ||||||||
\(914\) | −7.85641 | −0.259867 | ||||||||
\(915\) | −6.53590 | −0.216070 | ||||||||
\(916\) | −18.5359 | −0.612443 | ||||||||
\(917\) | 24.9282 | 0.823202 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.4256 | 1.69637 | 0.848187 | − | 0.529696i | \(-0.177694\pi\) | ||||
0.848187 | + | 0.529696i | \(0.177694\pi\) | |||||||
\(920\) | 6.00000 | 0.197814 | ||||||||
\(921\) | −32.3923 | −1.06736 | ||||||||
\(922\) | −10.3923 | −0.342252 | ||||||||
\(923\) | −3.21539 | −0.105836 | ||||||||
\(924\) | −12.9282 | −0.425307 | ||||||||
\(925\) | −6.19615 | −0.203728 | ||||||||
\(926\) | 61.5167 | 2.02156 | ||||||||
\(927\) | 9.85641 | 0.323727 | ||||||||
\(928\) | 42.5885 | 1.39803 | ||||||||
\(929\) | −1.60770 | −0.0527468 | −0.0263734 | − | 0.999652i | \(-0.508396\pi\) | ||||
−0.0263734 | + | 0.999652i | \(0.508396\pi\) | |||||||
\(930\) | −15.4641 | −0.507088 | ||||||||
\(931\) | 0.464102 | 0.0152103 | ||||||||
\(932\) | −7.85641 | −0.257345 | ||||||||
\(933\) | 32.4449 | 1.06220 | ||||||||
\(934\) | −35.5692 | −1.16386 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.26795 | 0.0414442 | ||||||||
\(937\) | −16.2487 | −0.530822 | −0.265411 | − | 0.964135i | \(-0.585508\pi\) | ||||
−0.265411 | + | 0.964135i | \(0.585508\pi\) | |||||||
\(938\) | 37.8564 | 1.23606 | ||||||||
\(939\) | 6.39230 | 0.208605 | ||||||||
\(940\) | −3.46410 | −0.112987 | ||||||||
\(941\) | 0.588457 | 0.0191832 | 0.00959158 | − | 0.999954i | \(-0.496947\pi\) | ||||
0.00959158 | + | 0.999954i | \(0.496947\pi\) | |||||||
\(942\) | −11.0718 | −0.360739 | ||||||||
\(943\) | 4.39230 | 0.143033 | ||||||||
\(944\) | −12.6795 | −0.412682 | ||||||||
\(945\) | −2.73205 | −0.0888736 | ||||||||
\(946\) | −34.3923 | −1.11819 | ||||||||
\(947\) | 28.1436 | 0.914544 | 0.457272 | − | 0.889327i | \(-0.348827\pi\) | ||||
0.457272 | + | 0.889327i | \(0.348827\pi\) | |||||||
\(948\) | −10.9282 | −0.354932 | ||||||||
\(949\) | −12.3923 | −0.402271 | ||||||||
\(950\) | −1.73205 | −0.0561951 | ||||||||
\(951\) | −11.3205 | −0.367093 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.8564 | 1.22629 | 0.613145 | − | 0.789971i | \(-0.289904\pi\) | ||||
0.613145 | + | 0.789971i | \(0.289904\pi\) | |||||||
\(954\) | 16.3923 | 0.530720 | ||||||||
\(955\) | 0.339746 | 0.0109939 | ||||||||
\(956\) | −9.80385 | −0.317079 | ||||||||
\(957\) | 38.7846 | 1.25373 | ||||||||
\(958\) | −44.1962 | −1.42791 | ||||||||
\(959\) | −54.2487 | −1.75178 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 48.7128 | 1.57138 | ||||||||
\(962\) | 7.85641 | 0.253301 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.07180 | −0.0989359 | ||||||||
\(965\) | 17.1244 | 0.551253 | ||||||||
\(966\) | 16.3923 | 0.527414 | ||||||||
\(967\) | 4.87564 | 0.156790 | 0.0783951 | − | 0.996922i | \(-0.475020\pi\) | ||||
0.0783951 | + | 0.996922i | \(0.475020\pi\) | |||||||
\(968\) | 19.7321 | 0.634212 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.7321 | 0.344585 | ||||||||
\(971\) | −27.7128 | −0.889346 | −0.444673 | − | 0.895693i | \(-0.646680\pi\) | ||||
−0.444673 | + | 0.895693i | \(0.646680\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 22.9282 | 0.735044 | ||||||||
\(974\) | 56.1051 | 1.79772 | ||||||||
\(975\) | 0.732051 | 0.0234444 | ||||||||
\(976\) | 32.6795 | 1.04605 | ||||||||
\(977\) | −39.0333 | −1.24879 | −0.624393 | − | 0.781110i | \(-0.714654\pi\) | ||||
−0.624393 | + | 0.781110i | \(0.714654\pi\) | |||||||
\(978\) | −16.0526 | −0.513304 | ||||||||
\(979\) | 50.7846 | 1.62308 | ||||||||
\(980\) | 0.464102 | 0.0148252 | ||||||||
\(981\) | −14.3923 | −0.459511 | ||||||||
\(982\) | −27.8038 | −0.887256 | ||||||||
\(983\) | −41.3205 | −1.31792 | −0.658960 | − | 0.752178i | \(-0.729003\pi\) | ||||
−0.658960 | + | 0.752178i | \(0.729003\pi\) | |||||||
\(984\) | 2.19615 | 0.0700108 | ||||||||
\(985\) | −24.0000 | −0.764704 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.46410 | 0.301246 | ||||||||
\(988\) | 0.732051 | 0.0232896 | ||||||||
\(989\) | 14.5359 | 0.462215 | ||||||||
\(990\) | −8.19615 | −0.260491 | ||||||||
\(991\) | 13.0718 | 0.415239 | 0.207620 | − | 0.978210i | \(-0.433428\pi\) | ||||
0.207620 | + | 0.978210i | \(0.433428\pi\) | |||||||
\(992\) | 46.3923 | 1.47296 | ||||||||
\(993\) | −25.7128 | −0.815971 | ||||||||
\(994\) | −20.7846 | −0.659248 | ||||||||
\(995\) | −15.3205 | −0.485693 | ||||||||
\(996\) | −12.9282 | −0.409646 | ||||||||
\(997\) | −17.6077 | −0.557641 | −0.278821 | − | 0.960343i | \(-0.589944\pi\) | ||||
−0.278821 | + | 0.960343i | \(0.589944\pi\) | |||||||
\(998\) | −18.2487 | −0.577653 | ||||||||
\(999\) | −6.19615 | −0.196038 |
(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 | 285.2.a.e.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 855.2.a.f.1.2 | 2 | |||
4.3 | odd | 2 | 4560.2.a.bh.1.2 | 2 | |||
5.2 | odd | 4 | 1425.2.c.k.799.1 | 4 | |||
5.3 | odd | 4 | 1425.2.c.k.799.4 | 4 | |||
5.4 | even | 2 | 1425.2.a.o.1.2 | 2 | |||
15.14 | odd | 2 | 4275.2.a.t.1.1 | 2 | |||
19.18 | odd | 2 | 5415.2.a.r.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.a.e.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
855.2.a.f.1.2 | 2 | 3.2 | odd | 2 | |||
1425.2.a.o.1.2 | 2 | 5.4 | even | 2 | |||
1425.2.c.k.799.1 | 4 | 5.2 | odd | 4 | |||
1425.2.c.k.799.4 | 4 | 5.3 | odd | 4 | |||
4275.2.a.t.1.1 | 2 | 15.14 | odd | 2 | |||
4560.2.a.bh.1.2 | 2 | 4.3 | odd | 2 | |||
5415.2.a.r.1.2 | 2 | 19.18 | odd | 2 |