Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-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 | ||||||||
\(3\) | 0.732051 | 0.422650 | 0.211325 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211325 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.73205 | 0.774597 | 0.387298 | − | 0.921954i | \(-0.373408\pi\) | ||||
0.387298 | + | 0.921954i | \(0.373408\pi\) | |||||||
\(6\) | −0.732051 | −0.298858 | ||||||||
\(7\) | 4.00000 | 1.51186 | 0.755929 | − | 0.654654i | \(-0.227186\pi\) | ||||
0.755929 | + | 0.654654i | \(0.227186\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | −1.73205 | −0.547723 | ||||||||
\(11\) | −4.73205 | −1.42677 | −0.713384 | − | 0.700774i | \(-0.752838\pi\) | ||||
−0.713384 | + | 0.700774i | \(0.752838\pi\) | |||||||
\(12\) | 0.732051 | 0.211325 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | −4.00000 | −1.06904 | ||||||||
\(15\) | 1.26795 | 0.327383 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.73205 | −0.420084 | −0.210042 | − | 0.977692i | \(-0.567360\pi\) | ||||
−0.210042 | + | 0.977692i | \(0.567360\pi\) | |||||||
\(18\) | 2.46410 | 0.580794 | ||||||||
\(19\) | 1.26795 | 0.290887 | 0.145444 | − | 0.989367i | \(-0.453539\pi\) | ||||
0.145444 | + | 0.989367i | \(0.453539\pi\) | |||||||
\(20\) | 1.73205 | 0.387298 | ||||||||
\(21\) | 2.92820 | 0.638986 | ||||||||
\(22\) | 4.73205 | 1.00888 | ||||||||
\(23\) | 1.26795 | 0.264386 | 0.132193 | − | 0.991224i | \(-0.457798\pi\) | ||||
0.132193 | + | 0.991224i | \(0.457798\pi\) | |||||||
\(24\) | −0.732051 | −0.149429 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | −6.00000 | −1.17670 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | 4.26795 | 0.792538 | 0.396269 | − | 0.918134i | \(-0.370305\pi\) | ||||
0.396269 | + | 0.918134i | \(0.370305\pi\) | |||||||
\(30\) | −1.26795 | −0.231495 | ||||||||
\(31\) | 1.26795 | 0.227730 | 0.113865 | − | 0.993496i | \(-0.463677\pi\) | ||||
0.113865 | + | 0.993496i | \(0.463677\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.46410 | −0.603023 | ||||||||
\(34\) | 1.73205 | 0.297044 | ||||||||
\(35\) | 6.92820 | 1.17108 | ||||||||
\(36\) | −2.46410 | −0.410684 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −1.26795 | −0.205689 | ||||||||
\(39\) | 4.39230 | 0.703332 | ||||||||
\(40\) | −1.73205 | −0.273861 | ||||||||
\(41\) | −0.464102 | −0.0724805 | −0.0362402 | − | 0.999343i | \(-0.511538\pi\) | ||||
−0.0362402 | + | 0.999343i | \(0.511538\pi\) | |||||||
\(42\) | −2.92820 | −0.451832 | ||||||||
\(43\) | 9.46410 | 1.44326 | 0.721631 | − | 0.692278i | \(-0.243393\pi\) | ||||
0.721631 | + | 0.692278i | \(0.243393\pi\) | |||||||
\(44\) | −4.73205 | −0.713384 | ||||||||
\(45\) | −4.26795 | −0.636228 | ||||||||
\(46\) | −1.26795 | −0.186949 | ||||||||
\(47\) | 11.6603 | 1.70082 | 0.850411 | − | 0.526118i | \(-0.176353\pi\) | ||||
0.850411 | + | 0.526118i | \(0.176353\pi\) | |||||||
\(48\) | 0.732051 | 0.105662 | ||||||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | 2.00000 | 0.282843 | ||||||||
\(51\) | −1.26795 | −0.177548 | ||||||||
\(52\) | 6.00000 | 0.832050 | ||||||||
\(53\) | −2.53590 | −0.348332 | −0.174166 | − | 0.984716i | \(-0.555723\pi\) | ||||
−0.174166 | + | 0.984716i | \(0.555723\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | −8.19615 | −1.10517 | ||||||||
\(56\) | −4.00000 | −0.534522 | ||||||||
\(57\) | 0.928203 | 0.122944 | ||||||||
\(58\) | −4.26795 | −0.560409 | ||||||||
\(59\) | −2.53590 | −0.330146 | −0.165073 | − | 0.986281i | \(-0.552786\pi\) | ||||
−0.165073 | + | 0.986281i | \(0.552786\pi\) | |||||||
\(60\) | 1.26795 | 0.163692 | ||||||||
\(61\) | 14.6603 | 1.87705 | 0.938527 | − | 0.345207i | \(-0.112191\pi\) | ||||
0.938527 | + | 0.345207i | \(0.112191\pi\) | |||||||
\(62\) | −1.26795 | −0.161030 | ||||||||
\(63\) | −9.85641 | −1.24179 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.3923 | 1.28901 | ||||||||
\(66\) | 3.46410 | 0.426401 | ||||||||
\(67\) | −6.19615 | −0.756980 | −0.378490 | − | 0.925605i | \(-0.623557\pi\) | ||||
−0.378490 | + | 0.925605i | \(0.623557\pi\) | |||||||
\(68\) | −1.73205 | −0.210042 | ||||||||
\(69\) | 0.928203 | 0.111743 | ||||||||
\(70\) | −6.92820 | −0.828079 | ||||||||
\(71\) | 2.53590 | 0.300956 | 0.150478 | − | 0.988613i | \(-0.451919\pi\) | ||||
0.150478 | + | 0.988613i | \(0.451919\pi\) | |||||||
\(72\) | 2.46410 | 0.290397 | ||||||||
\(73\) | 12.3923 | 1.45041 | 0.725205 | − | 0.688533i | \(-0.241745\pi\) | ||||
0.725205 | + | 0.688533i | \(0.241745\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.46410 | −0.169060 | ||||||||
\(76\) | 1.26795 | 0.145444 | ||||||||
\(77\) | −18.9282 | −2.15707 | ||||||||
\(78\) | −4.39230 | −0.497331 | ||||||||
\(79\) | 8.19615 | 0.922139 | 0.461070 | − | 0.887364i | \(-0.347466\pi\) | ||||
0.461070 | + | 0.887364i | \(0.347466\pi\) | |||||||
\(80\) | 1.73205 | 0.193649 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0.464102 | 0.0512514 | ||||||||
\(83\) | 11.6603 | 1.27988 | 0.639940 | − | 0.768425i | \(-0.278959\pi\) | ||||
0.639940 | + | 0.768425i | \(0.278959\pi\) | |||||||
\(84\) | 2.92820 | 0.319493 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | −9.46410 | −1.02054 | ||||||||
\(87\) | 3.12436 | 0.334966 | ||||||||
\(88\) | 4.73205 | 0.504438 | ||||||||
\(89\) | −5.19615 | −0.550791 | −0.275396 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275396 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(90\) | 4.26795 | 0.449881 | ||||||||
\(91\) | 24.0000 | 2.51588 | ||||||||
\(92\) | 1.26795 | 0.132193 | ||||||||
\(93\) | 0.928203 | 0.0962502 | ||||||||
\(94\) | −11.6603 | −1.20266 | ||||||||
\(95\) | 2.19615 | 0.225320 | ||||||||
\(96\) | −0.732051 | −0.0747146 | ||||||||
\(97\) | 5.19615 | 0.527589 | 0.263795 | − | 0.964579i | \(-0.415026\pi\) | ||||
0.263795 | + | 0.964579i | \(0.415026\pi\) | |||||||
\(98\) | −9.00000 | −0.909137 | ||||||||
\(99\) | 11.6603 | 1.17190 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | 0.464102 | 0.0461798 | 0.0230899 | − | 0.999733i | \(-0.492650\pi\) | ||||
0.0230899 | + | 0.999733i | \(0.492650\pi\) | |||||||
\(102\) | 1.26795 | 0.125546 | ||||||||
\(103\) | −6.92820 | −0.682656 | −0.341328 | − | 0.939944i | \(-0.610877\pi\) | ||||
−0.341328 | + | 0.939944i | \(0.610877\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 5.07180 | 0.494957 | ||||||||
\(106\) | 2.53590 | 0.246308 | ||||||||
\(107\) | −16.3923 | −1.58470 | −0.792352 | − | 0.610064i | \(-0.791144\pi\) | ||||
−0.792352 | + | 0.610064i | \(0.791144\pi\) | |||||||
\(108\) | −4.00000 | −0.384900 | ||||||||
\(109\) | −7.73205 | −0.740596 | −0.370298 | − | 0.928913i | \(-0.620744\pi\) | ||||
−0.370298 | + | 0.928913i | \(0.620744\pi\) | |||||||
\(110\) | 8.19615 | 0.781472 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | −19.8564 | −1.86793 | −0.933967 | − | 0.357360i | \(-0.883677\pi\) | ||||
−0.933967 | + | 0.357360i | \(0.883677\pi\) | |||||||
\(114\) | −0.928203 | −0.0869342 | ||||||||
\(115\) | 2.19615 | 0.204792 | ||||||||
\(116\) | 4.26795 | 0.396269 | ||||||||
\(117\) | −14.7846 | −1.36684 | ||||||||
\(118\) | 2.53590 | 0.233448 | ||||||||
\(119\) | −6.92820 | −0.635107 | ||||||||
\(120\) | −1.26795 | −0.115747 | ||||||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | −14.6603 | −1.32728 | ||||||||
\(123\) | −0.339746 | −0.0306339 | ||||||||
\(124\) | 1.26795 | 0.113865 | ||||||||
\(125\) | −12.1244 | −1.08444 | ||||||||
\(126\) | 9.85641 | 0.878078 | ||||||||
\(127\) | −10.5885 | −0.939574 | −0.469787 | − | 0.882780i | \(-0.655669\pi\) | ||||
−0.469787 | + | 0.882780i | \(0.655669\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.92820 | 0.609994 | ||||||||
\(130\) | −10.3923 | −0.911465 | ||||||||
\(131\) | 8.19615 | 0.716101 | 0.358051 | − | 0.933702i | \(-0.383442\pi\) | ||||
0.358051 | + | 0.933702i | \(0.383442\pi\) | |||||||
\(132\) | −3.46410 | −0.301511 | ||||||||
\(133\) | 5.07180 | 0.439781 | ||||||||
\(134\) | 6.19615 | 0.535266 | ||||||||
\(135\) | −6.92820 | −0.596285 | ||||||||
\(136\) | 1.73205 | 0.148522 | ||||||||
\(137\) | −13.3923 | −1.14418 | −0.572091 | − | 0.820190i | \(-0.693868\pi\) | ||||
−0.572091 | + | 0.820190i | \(0.693868\pi\) | |||||||
\(138\) | −0.928203 | −0.0790139 | ||||||||
\(139\) | −1.80385 | −0.153000 | −0.0765002 | − | 0.997070i | \(-0.524375\pi\) | ||||
−0.0765002 | + | 0.997070i | \(0.524375\pi\) | |||||||
\(140\) | 6.92820 | 0.585540 | ||||||||
\(141\) | 8.53590 | 0.718852 | ||||||||
\(142\) | −2.53590 | −0.212808 | ||||||||
\(143\) | −28.3923 | −2.37428 | ||||||||
\(144\) | −2.46410 | −0.205342 | ||||||||
\(145\) | 7.39230 | 0.613898 | ||||||||
\(146\) | −12.3923 | −1.02559 | ||||||||
\(147\) | 6.58846 | 0.543407 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.92820 | 0.321811 | 0.160905 | − | 0.986970i | \(-0.448559\pi\) | ||||
0.160905 | + | 0.986970i | \(0.448559\pi\) | |||||||
\(150\) | 1.46410 | 0.119543 | ||||||||
\(151\) | 1.80385 | 0.146795 | 0.0733975 | − | 0.997303i | \(-0.476616\pi\) | ||||
0.0733975 | + | 0.997303i | \(0.476616\pi\) | |||||||
\(152\) | −1.26795 | −0.102844 | ||||||||
\(153\) | 4.26795 | 0.345043 | ||||||||
\(154\) | 18.9282 | 1.52528 | ||||||||
\(155\) | 2.19615 | 0.176399 | ||||||||
\(156\) | 4.39230 | 0.351666 | ||||||||
\(157\) | −9.39230 | −0.749588 | −0.374794 | − | 0.927108i | \(-0.622286\pi\) | ||||
−0.374794 | + | 0.927108i | \(0.622286\pi\) | |||||||
\(158\) | −8.19615 | −0.652051 | ||||||||
\(159\) | −1.85641 | −0.147223 | ||||||||
\(160\) | −1.73205 | −0.136931 | ||||||||
\(161\) | 5.07180 | 0.399714 | ||||||||
\(162\) | −4.46410 | −0.350733 | ||||||||
\(163\) | 2.53590 | 0.198627 | 0.0993134 | − | 0.995056i | \(-0.468335\pi\) | ||||
0.0993134 | + | 0.995056i | \(0.468335\pi\) | |||||||
\(164\) | −0.464102 | −0.0362402 | ||||||||
\(165\) | −6.00000 | −0.467099 | ||||||||
\(166\) | −11.6603 | −0.905011 | ||||||||
\(167\) | 6.92820 | 0.536120 | 0.268060 | − | 0.963402i | \(-0.413617\pi\) | ||||
0.268060 | + | 0.963402i | \(0.413617\pi\) | |||||||
\(168\) | −2.92820 | −0.225916 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 3.00000 | 0.230089 | ||||||||
\(171\) | −3.12436 | −0.238925 | ||||||||
\(172\) | 9.46410 | 0.721631 | ||||||||
\(173\) | 9.92820 | 0.754827 | 0.377414 | − | 0.926045i | \(-0.376813\pi\) | ||||
0.377414 | + | 0.926045i | \(0.376813\pi\) | |||||||
\(174\) | −3.12436 | −0.236857 | ||||||||
\(175\) | −8.00000 | −0.604743 | ||||||||
\(176\) | −4.73205 | −0.356692 | ||||||||
\(177\) | −1.85641 | −0.139536 | ||||||||
\(178\) | 5.19615 | 0.389468 | ||||||||
\(179\) | 11.3205 | 0.846135 | 0.423067 | − | 0.906098i | \(-0.360953\pi\) | ||||
0.423067 | + | 0.906098i | \(0.360953\pi\) | |||||||
\(180\) | −4.26795 | −0.318114 | ||||||||
\(181\) | −15.3923 | −1.14410 | −0.572051 | − | 0.820218i | \(-0.693852\pi\) | ||||
−0.572051 | + | 0.820218i | \(0.693852\pi\) | |||||||
\(182\) | −24.0000 | −1.77900 | ||||||||
\(183\) | 10.7321 | 0.793336 | ||||||||
\(184\) | −1.26795 | −0.0934745 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.928203 | −0.0680592 | ||||||||
\(187\) | 8.19615 | 0.599362 | ||||||||
\(188\) | 11.6603 | 0.850411 | ||||||||
\(189\) | −16.0000 | −1.16383 | ||||||||
\(190\) | −2.19615 | −0.159326 | ||||||||
\(191\) | 24.5885 | 1.77916 | 0.889579 | − | 0.456781i | \(-0.150998\pi\) | ||||
0.889579 | + | 0.456781i | \(0.150998\pi\) | |||||||
\(192\) | 0.732051 | 0.0528312 | ||||||||
\(193\) | −12.1244 | −0.872730 | −0.436365 | − | 0.899770i | \(-0.643734\pi\) | ||||
−0.436365 | + | 0.899770i | \(0.643734\pi\) | |||||||
\(194\) | −5.19615 | −0.373062 | ||||||||
\(195\) | 7.60770 | 0.544798 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | 26.3205 | 1.87526 | 0.937629 | − | 0.347637i | \(-0.113016\pi\) | ||||
0.937629 | + | 0.347637i | \(0.113016\pi\) | |||||||
\(198\) | −11.6603 | −0.828658 | ||||||||
\(199\) | 5.07180 | 0.359530 | 0.179765 | − | 0.983710i | \(-0.442466\pi\) | ||||
0.179765 | + | 0.983710i | \(0.442466\pi\) | |||||||
\(200\) | 2.00000 | 0.141421 | ||||||||
\(201\) | −4.53590 | −0.319938 | ||||||||
\(202\) | −0.464102 | −0.0326541 | ||||||||
\(203\) | 17.0718 | 1.19821 | ||||||||
\(204\) | −1.26795 | −0.0887742 | ||||||||
\(205\) | −0.803848 | −0.0561432 | ||||||||
\(206\) | 6.92820 | 0.482711 | ||||||||
\(207\) | −3.12436 | −0.217158 | ||||||||
\(208\) | 6.00000 | 0.416025 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | −5.07180 | −0.349987 | ||||||||
\(211\) | 12.3923 | 0.853121 | 0.426561 | − | 0.904459i | \(-0.359725\pi\) | ||||
0.426561 | + | 0.904459i | \(0.359725\pi\) | |||||||
\(212\) | −2.53590 | −0.174166 | ||||||||
\(213\) | 1.85641 | 0.127199 | ||||||||
\(214\) | 16.3923 | 1.12055 | ||||||||
\(215\) | 16.3923 | 1.11795 | ||||||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | 5.07180 | 0.344296 | ||||||||
\(218\) | 7.73205 | 0.523681 | ||||||||
\(219\) | 9.07180 | 0.613015 | ||||||||
\(220\) | −8.19615 | −0.552584 | ||||||||
\(221\) | −10.3923 | −0.699062 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.5885 | −1.51263 | −0.756317 | − | 0.654205i | \(-0.773003\pi\) | ||||
−0.756317 | + | 0.654205i | \(0.773003\pi\) | |||||||
\(224\) | −4.00000 | −0.267261 | ||||||||
\(225\) | 4.92820 | 0.328547 | ||||||||
\(226\) | 19.8564 | 1.32083 | ||||||||
\(227\) | 1.26795 | 0.0841567 | 0.0420784 | − | 0.999114i | \(-0.486602\pi\) | ||||
0.0420784 | + | 0.999114i | \(0.486602\pi\) | |||||||
\(228\) | 0.928203 | 0.0614718 | ||||||||
\(229\) | −19.0000 | −1.25556 | −0.627778 | − | 0.778393i | \(-0.716035\pi\) | ||||
−0.627778 | + | 0.778393i | \(0.716035\pi\) | |||||||
\(230\) | −2.19615 | −0.144810 | ||||||||
\(231\) | −13.8564 | −0.911685 | ||||||||
\(232\) | −4.26795 | −0.280205 | ||||||||
\(233\) | 4.60770 | 0.301860 | 0.150930 | − | 0.988544i | \(-0.451773\pi\) | ||||
0.150930 | + | 0.988544i | \(0.451773\pi\) | |||||||
\(234\) | 14.7846 | 0.966500 | ||||||||
\(235\) | 20.1962 | 1.31745 | ||||||||
\(236\) | −2.53590 | −0.165073 | ||||||||
\(237\) | 6.00000 | 0.389742 | ||||||||
\(238\) | 6.92820 | 0.449089 | ||||||||
\(239\) | −5.07180 | −0.328067 | −0.164034 | − | 0.986455i | \(-0.552451\pi\) | ||||
−0.164034 | + | 0.986455i | \(0.552451\pi\) | |||||||
\(240\) | 1.26795 | 0.0818458 | ||||||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | −11.3923 | −0.732325 | ||||||||
\(243\) | 15.2679 | 0.979439 | ||||||||
\(244\) | 14.6603 | 0.938527 | ||||||||
\(245\) | 15.5885 | 0.995910 | ||||||||
\(246\) | 0.339746 | 0.0216614 | ||||||||
\(247\) | 7.60770 | 0.484066 | ||||||||
\(248\) | −1.26795 | −0.0805149 | ||||||||
\(249\) | 8.53590 | 0.540941 | ||||||||
\(250\) | 12.1244 | 0.766812 | ||||||||
\(251\) | 5.07180 | 0.320129 | 0.160064 | − | 0.987107i | \(-0.448830\pi\) | ||||
0.160064 | + | 0.987107i | \(0.448830\pi\) | |||||||
\(252\) | −9.85641 | −0.620895 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 10.5885 | 0.664379 | ||||||||
\(255\) | −2.19615 | −0.137528 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.1962 | 0.698397 | 0.349198 | − | 0.937049i | \(-0.386454\pi\) | ||||
0.349198 | + | 0.937049i | \(0.386454\pi\) | |||||||
\(258\) | −6.92820 | −0.431331 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 10.3923 | 0.644503 | ||||||||
\(261\) | −10.5167 | −0.650965 | ||||||||
\(262\) | −8.19615 | −0.506360 | ||||||||
\(263\) | −23.3205 | −1.43800 | −0.719002 | − | 0.695008i | \(-0.755401\pi\) | ||||
−0.719002 | + | 0.695008i | \(0.755401\pi\) | |||||||
\(264\) | 3.46410 | 0.213201 | ||||||||
\(265\) | −4.39230 | −0.269817 | ||||||||
\(266\) | −5.07180 | −0.310972 | ||||||||
\(267\) | −3.80385 | −0.232792 | ||||||||
\(268\) | −6.19615 | −0.378490 | ||||||||
\(269\) | −7.60770 | −0.463849 | −0.231925 | − | 0.972734i | \(-0.574502\pi\) | ||||
−0.231925 | + | 0.972734i | \(0.574502\pi\) | |||||||
\(270\) | 6.92820 | 0.421637 | ||||||||
\(271\) | −14.5885 | −0.886186 | −0.443093 | − | 0.896476i | \(-0.646119\pi\) | ||||
−0.443093 | + | 0.896476i | \(0.646119\pi\) | |||||||
\(272\) | −1.73205 | −0.105021 | ||||||||
\(273\) | 17.5692 | 1.06334 | ||||||||
\(274\) | 13.3923 | 0.809059 | ||||||||
\(275\) | 9.46410 | 0.570707 | ||||||||
\(276\) | 0.928203 | 0.0558713 | ||||||||
\(277\) | −6.80385 | −0.408804 | −0.204402 | − | 0.978887i | \(-0.565525\pi\) | ||||
−0.204402 | + | 0.978887i | \(0.565525\pi\) | |||||||
\(278\) | 1.80385 | 0.108188 | ||||||||
\(279\) | −3.12436 | −0.187050 | ||||||||
\(280\) | −6.92820 | −0.414039 | ||||||||
\(281\) | −11.1962 | −0.667906 | −0.333953 | − | 0.942590i | \(-0.608383\pi\) | ||||
−0.333953 | + | 0.942590i | \(0.608383\pi\) | |||||||
\(282\) | −8.53590 | −0.508305 | ||||||||
\(283\) | 2.53590 | 0.150744 | 0.0753718 | − | 0.997156i | \(-0.475986\pi\) | ||||
0.0753718 | + | 0.997156i | \(0.475986\pi\) | |||||||
\(284\) | 2.53590 | 0.150478 | ||||||||
\(285\) | 1.60770 | 0.0952316 | ||||||||
\(286\) | 28.3923 | 1.67887 | ||||||||
\(287\) | −1.85641 | −0.109580 | ||||||||
\(288\) | 2.46410 | 0.145199 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | −7.39230 | −0.434091 | ||||||||
\(291\) | 3.80385 | 0.222985 | ||||||||
\(292\) | 12.3923 | 0.725205 | ||||||||
\(293\) | 25.3923 | 1.48343 | 0.741717 | − | 0.670713i | \(-0.234012\pi\) | ||||
0.741717 | + | 0.670713i | \(0.234012\pi\) | |||||||
\(294\) | −6.58846 | −0.384247 | ||||||||
\(295\) | −4.39230 | −0.255730 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.9282 | 1.09833 | ||||||||
\(298\) | −3.92820 | −0.227555 | ||||||||
\(299\) | 7.60770 | 0.439964 | ||||||||
\(300\) | −1.46410 | −0.0845299 | ||||||||
\(301\) | 37.8564 | 2.18201 | ||||||||
\(302\) | −1.80385 | −0.103800 | ||||||||
\(303\) | 0.339746 | 0.0195179 | ||||||||
\(304\) | 1.26795 | 0.0727219 | ||||||||
\(305\) | 25.3923 | 1.45396 | ||||||||
\(306\) | −4.26795 | −0.243982 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | −18.9282 | −1.07853 | ||||||||
\(309\) | −5.07180 | −0.288524 | ||||||||
\(310\) | −2.19615 | −0.124733 | ||||||||
\(311\) | −16.3923 | −0.929522 | −0.464761 | − | 0.885436i | \(-0.653860\pi\) | ||||
−0.464761 | + | 0.885436i | \(0.653860\pi\) | |||||||
\(312\) | −4.39230 | −0.248665 | ||||||||
\(313\) | 21.5885 | 1.22025 | 0.610126 | − | 0.792304i | \(-0.291119\pi\) | ||||
0.610126 | + | 0.792304i | \(0.291119\pi\) | |||||||
\(314\) | 9.39230 | 0.530038 | ||||||||
\(315\) | −17.0718 | −0.961887 | ||||||||
\(316\) | 8.19615 | 0.461070 | ||||||||
\(317\) | −9.00000 | −0.505490 | −0.252745 | − | 0.967533i | \(-0.581333\pi\) | ||||
−0.252745 | + | 0.967533i | \(0.581333\pi\) | |||||||
\(318\) | 1.85641 | 0.104102 | ||||||||
\(319\) | −20.1962 | −1.13077 | ||||||||
\(320\) | 1.73205 | 0.0968246 | ||||||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | −5.07180 | −0.282640 | ||||||||
\(323\) | −2.19615 | −0.122197 | ||||||||
\(324\) | 4.46410 | 0.248006 | ||||||||
\(325\) | −12.0000 | −0.665640 | ||||||||
\(326\) | −2.53590 | −0.140450 | ||||||||
\(327\) | −5.66025 | −0.313013 | ||||||||
\(328\) | 0.464102 | 0.0256257 | ||||||||
\(329\) | 46.6410 | 2.57140 | ||||||||
\(330\) | 6.00000 | 0.330289 | ||||||||
\(331\) | −30.9282 | −1.69997 | −0.849984 | − | 0.526809i | \(-0.823388\pi\) | ||||
−0.849984 | + | 0.526809i | \(0.823388\pi\) | |||||||
\(332\) | 11.6603 | 0.639940 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.92820 | −0.379094 | ||||||||
\(335\) | −10.7321 | −0.586355 | ||||||||
\(336\) | 2.92820 | 0.159747 | ||||||||
\(337\) | 7.00000 | 0.381314 | 0.190657 | − | 0.981657i | \(-0.438938\pi\) | ||||
0.190657 | + | 0.981657i | \(0.438938\pi\) | |||||||
\(338\) | −23.0000 | −1.25104 | ||||||||
\(339\) | −14.5359 | −0.789482 | ||||||||
\(340\) | −3.00000 | −0.162698 | ||||||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | 3.12436 | 0.168946 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | −9.46410 | −0.510270 | ||||||||
\(345\) | 1.60770 | 0.0865554 | ||||||||
\(346\) | −9.92820 | −0.533744 | ||||||||
\(347\) | −10.0526 | −0.539650 | −0.269825 | − | 0.962909i | \(-0.586966\pi\) | ||||
−0.269825 | + | 0.962909i | \(0.586966\pi\) | |||||||
\(348\) | 3.12436 | 0.167483 | ||||||||
\(349\) | −6.60770 | −0.353702 | −0.176851 | − | 0.984238i | \(-0.556591\pi\) | ||||
−0.176851 | + | 0.984238i | \(0.556591\pi\) | |||||||
\(350\) | 8.00000 | 0.427618 | ||||||||
\(351\) | −24.0000 | −1.28103 | ||||||||
\(352\) | 4.73205 | 0.252219 | ||||||||
\(353\) | −30.1244 | −1.60336 | −0.801679 | − | 0.597755i | \(-0.796060\pi\) | ||||
−0.801679 | + | 0.597755i | \(0.796060\pi\) | |||||||
\(354\) | 1.85641 | 0.0986669 | ||||||||
\(355\) | 4.39230 | 0.233119 | ||||||||
\(356\) | −5.19615 | −0.275396 | ||||||||
\(357\) | −5.07180 | −0.268428 | ||||||||
\(358\) | −11.3205 | −0.598307 | ||||||||
\(359\) | 33.4641 | 1.76617 | 0.883084 | − | 0.469215i | \(-0.155463\pi\) | ||||
0.883084 | + | 0.469215i | \(0.155463\pi\) | |||||||
\(360\) | 4.26795 | 0.224941 | ||||||||
\(361\) | −17.3923 | −0.915384 | ||||||||
\(362\) | 15.3923 | 0.809002 | ||||||||
\(363\) | 8.33975 | 0.437723 | ||||||||
\(364\) | 24.0000 | 1.25794 | ||||||||
\(365\) | 21.4641 | 1.12348 | ||||||||
\(366\) | −10.7321 | −0.560973 | ||||||||
\(367\) | 0.392305 | 0.0204781 | 0.0102391 | − | 0.999948i | \(-0.496741\pi\) | ||||
0.0102391 | + | 0.999948i | \(0.496741\pi\) | |||||||
\(368\) | 1.26795 | 0.0660964 | ||||||||
\(369\) | 1.14359 | 0.0595331 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.1436 | −0.526629 | ||||||||
\(372\) | 0.928203 | 0.0481251 | ||||||||
\(373\) | 19.7846 | 1.02441 | 0.512204 | − | 0.858864i | \(-0.328829\pi\) | ||||
0.512204 | + | 0.858864i | \(0.328829\pi\) | |||||||
\(374\) | −8.19615 | −0.423813 | ||||||||
\(375\) | −8.87564 | −0.458336 | ||||||||
\(376\) | −11.6603 | −0.601332 | ||||||||
\(377\) | 25.6077 | 1.31886 | ||||||||
\(378\) | 16.0000 | 0.822951 | ||||||||
\(379\) | 24.7846 | 1.27310 | 0.636550 | − | 0.771235i | \(-0.280361\pi\) | ||||
0.636550 | + | 0.771235i | \(0.280361\pi\) | |||||||
\(380\) | 2.19615 | 0.112660 | ||||||||
\(381\) | −7.75129 | −0.397111 | ||||||||
\(382\) | −24.5885 | −1.25805 | ||||||||
\(383\) | −25.8564 | −1.32120 | −0.660600 | − | 0.750738i | \(-0.729698\pi\) | ||||
−0.660600 | + | 0.750738i | \(0.729698\pi\) | |||||||
\(384\) | −0.732051 | −0.0373573 | ||||||||
\(385\) | −32.7846 | −1.67086 | ||||||||
\(386\) | 12.1244 | 0.617113 | ||||||||
\(387\) | −23.3205 | −1.18545 | ||||||||
\(388\) | 5.19615 | 0.263795 | ||||||||
\(389\) | −0.803848 | −0.0407567 | −0.0203783 | − | 0.999792i | \(-0.506487\pi\) | ||||
−0.0203783 | + | 0.999792i | \(0.506487\pi\) | |||||||
\(390\) | −7.60770 | −0.385231 | ||||||||
\(391\) | −2.19615 | −0.111064 | ||||||||
\(392\) | −9.00000 | −0.454569 | ||||||||
\(393\) | 6.00000 | 0.302660 | ||||||||
\(394\) | −26.3205 | −1.32601 | ||||||||
\(395\) | 14.1962 | 0.714286 | ||||||||
\(396\) | 11.6603 | 0.585950 | ||||||||
\(397\) | 5.00000 | 0.250943 | 0.125471 | − | 0.992097i | \(-0.459956\pi\) | ||||
0.125471 | + | 0.992097i | \(0.459956\pi\) | |||||||
\(398\) | −5.07180 | −0.254226 | ||||||||
\(399\) | 3.71281 | 0.185873 | ||||||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | 14.7846 | 0.738308 | 0.369154 | − | 0.929368i | \(-0.379647\pi\) | ||||
0.369154 | + | 0.929368i | \(0.379647\pi\) | |||||||
\(402\) | 4.53590 | 0.226230 | ||||||||
\(403\) | 7.60770 | 0.378966 | ||||||||
\(404\) | 0.464102 | 0.0230899 | ||||||||
\(405\) | 7.73205 | 0.384209 | ||||||||
\(406\) | −17.0718 | −0.847259 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.26795 | 0.0627728 | ||||||||
\(409\) | 33.5885 | 1.66084 | 0.830421 | − | 0.557136i | \(-0.188100\pi\) | ||||
0.830421 | + | 0.557136i | \(0.188100\pi\) | |||||||
\(410\) | 0.803848 | 0.0396992 | ||||||||
\(411\) | −9.80385 | −0.483588 | ||||||||
\(412\) | −6.92820 | −0.341328 | ||||||||
\(413\) | −10.1436 | −0.499134 | ||||||||
\(414\) | 3.12436 | 0.153554 | ||||||||
\(415\) | 20.1962 | 0.991390 | ||||||||
\(416\) | −6.00000 | −0.294174 | ||||||||
\(417\) | −1.32051 | −0.0646656 | ||||||||
\(418\) | 6.00000 | 0.293470 | ||||||||
\(419\) | 10.1436 | 0.495547 | 0.247773 | − | 0.968818i | \(-0.420301\pi\) | ||||
0.247773 | + | 0.968818i | \(0.420301\pi\) | |||||||
\(420\) | 5.07180 | 0.247478 | ||||||||
\(421\) | −3.33975 | −0.162769 | −0.0813846 | − | 0.996683i | \(-0.525934\pi\) | ||||
−0.0813846 | + | 0.996683i | \(0.525934\pi\) | |||||||
\(422\) | −12.3923 | −0.603248 | ||||||||
\(423\) | −28.7321 | −1.39700 | ||||||||
\(424\) | 2.53590 | 0.123154 | ||||||||
\(425\) | 3.46410 | 0.168034 | ||||||||
\(426\) | −1.85641 | −0.0899432 | ||||||||
\(427\) | 58.6410 | 2.83784 | ||||||||
\(428\) | −16.3923 | −0.792352 | ||||||||
\(429\) | −20.7846 | −1.00349 | ||||||||
\(430\) | −16.3923 | −0.790507 | ||||||||
\(431\) | 22.0526 | 1.06223 | 0.531117 | − | 0.847298i | \(-0.321772\pi\) | ||||
0.531117 | + | 0.847298i | \(0.321772\pi\) | |||||||
\(432\) | −4.00000 | −0.192450 | ||||||||
\(433\) | −12.6077 | −0.605887 | −0.302944 | − | 0.953008i | \(-0.597969\pi\) | ||||
−0.302944 | + | 0.953008i | \(0.597969\pi\) | |||||||
\(434\) | −5.07180 | −0.243454 | ||||||||
\(435\) | 5.41154 | 0.259464 | ||||||||
\(436\) | −7.73205 | −0.370298 | ||||||||
\(437\) | 1.60770 | 0.0769065 | ||||||||
\(438\) | −9.07180 | −0.433467 | ||||||||
\(439\) | 2.53590 | 0.121032 | 0.0605159 | − | 0.998167i | \(-0.480725\pi\) | ||||
0.0605159 | + | 0.998167i | \(0.480725\pi\) | |||||||
\(440\) | 8.19615 | 0.390736 | ||||||||
\(441\) | −22.1769 | −1.05604 | ||||||||
\(442\) | 10.3923 | 0.494312 | ||||||||
\(443\) | 9.46410 | 0.449653 | 0.224827 | − | 0.974399i | \(-0.427818\pi\) | ||||
0.224827 | + | 0.974399i | \(0.427818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | −0.426641 | ||||||||
\(446\) | 22.5885 | 1.06959 | ||||||||
\(447\) | 2.87564 | 0.136013 | ||||||||
\(448\) | 4.00000 | 0.188982 | ||||||||
\(449\) | −11.0718 | −0.522510 | −0.261255 | − | 0.965270i | \(-0.584136\pi\) | ||||
−0.261255 | + | 0.965270i | \(0.584136\pi\) | |||||||
\(450\) | −4.92820 | −0.232318 | ||||||||
\(451\) | 2.19615 | 0.103413 | ||||||||
\(452\) | −19.8564 | −0.933967 | ||||||||
\(453\) | 1.32051 | 0.0620429 | ||||||||
\(454\) | −1.26795 | −0.0595078 | ||||||||
\(455\) | 41.5692 | 1.94880 | ||||||||
\(456\) | −0.928203 | −0.0434671 | ||||||||
\(457\) | −31.9808 | −1.49600 | −0.747998 | − | 0.663700i | \(-0.768985\pi\) | ||||
−0.747998 | + | 0.663700i | \(0.768985\pi\) | |||||||
\(458\) | 19.0000 | 0.887812 | ||||||||
\(459\) | 6.92820 | 0.323381 | ||||||||
\(460\) | 2.19615 | 0.102396 | ||||||||
\(461\) | −21.7128 | −1.01127 | −0.505633 | − | 0.862749i | \(-0.668741\pi\) | ||||
−0.505633 | + | 0.862749i | \(0.668741\pi\) | |||||||
\(462\) | 13.8564 | 0.644658 | ||||||||
\(463\) | −21.4641 | −0.997521 | −0.498761 | − | 0.866740i | \(-0.666211\pi\) | ||||
−0.498761 | + | 0.866740i | \(0.666211\pi\) | |||||||
\(464\) | 4.26795 | 0.198135 | ||||||||
\(465\) | 1.60770 | 0.0745551 | ||||||||
\(466\) | −4.60770 | −0.213447 | ||||||||
\(467\) | −18.2487 | −0.844450 | −0.422225 | − | 0.906491i | \(-0.638751\pi\) | ||||
−0.422225 | + | 0.906491i | \(0.638751\pi\) | |||||||
\(468\) | −14.7846 | −0.683419 | ||||||||
\(469\) | −24.7846 | −1.14445 | ||||||||
\(470\) | −20.1962 | −0.931579 | ||||||||
\(471\) | −6.87564 | −0.316813 | ||||||||
\(472\) | 2.53590 | 0.116724 | ||||||||
\(473\) | −44.7846 | −2.05920 | ||||||||
\(474\) | −6.00000 | −0.275589 | ||||||||
\(475\) | −2.53590 | −0.116355 | ||||||||
\(476\) | −6.92820 | −0.317554 | ||||||||
\(477\) | 6.24871 | 0.286109 | ||||||||
\(478\) | 5.07180 | 0.231979 | ||||||||
\(479\) | 2.53590 | 0.115868 | 0.0579341 | − | 0.998320i | \(-0.481549\pi\) | ||||
0.0579341 | + | 0.998320i | \(0.481549\pi\) | |||||||
\(480\) | −1.26795 | −0.0578737 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −18.0000 | −0.819878 | ||||||||
\(483\) | 3.71281 | 0.168939 | ||||||||
\(484\) | 11.3923 | 0.517832 | ||||||||
\(485\) | 9.00000 | 0.408669 | ||||||||
\(486\) | −15.2679 | −0.692568 | ||||||||
\(487\) | −10.0526 | −0.455525 | −0.227762 | − | 0.973717i | \(-0.573141\pi\) | ||||
−0.227762 | + | 0.973717i | \(0.573141\pi\) | |||||||
\(488\) | −14.6603 | −0.663639 | ||||||||
\(489\) | 1.85641 | 0.0839496 | ||||||||
\(490\) | −15.5885 | −0.704215 | ||||||||
\(491\) | −22.9808 | −1.03711 | −0.518554 | − | 0.855045i | \(-0.673529\pi\) | ||||
−0.518554 | + | 0.855045i | \(0.673529\pi\) | |||||||
\(492\) | −0.339746 | −0.0153169 | ||||||||
\(493\) | −7.39230 | −0.332933 | ||||||||
\(494\) | −7.60770 | −0.342286 | ||||||||
\(495\) | 20.1962 | 0.907750 | ||||||||
\(496\) | 1.26795 | 0.0569326 | ||||||||
\(497\) | 10.1436 | 0.455002 | ||||||||
\(498\) | −8.53590 | −0.382503 | ||||||||
\(499\) | 8.19615 | 0.366910 | 0.183455 | − | 0.983028i | \(-0.441272\pi\) | ||||
0.183455 | + | 0.983028i | \(0.441272\pi\) | |||||||
\(500\) | −12.1244 | −0.542218 | ||||||||
\(501\) | 5.07180 | 0.226591 | ||||||||
\(502\) | −5.07180 | −0.226365 | ||||||||
\(503\) | 12.5885 | 0.561292 | 0.280646 | − | 0.959811i | \(-0.409451\pi\) | ||||
0.280646 | + | 0.959811i | \(0.409451\pi\) | |||||||
\(504\) | 9.85641 | 0.439039 | ||||||||
\(505\) | 0.803848 | 0.0357707 | ||||||||
\(506\) | 6.00000 | 0.266733 | ||||||||
\(507\) | 16.8372 | 0.747765 | ||||||||
\(508\) | −10.5885 | −0.469787 | ||||||||
\(509\) | −31.6410 | −1.40246 | −0.701232 | − | 0.712933i | \(-0.747366\pi\) | ||||
−0.701232 | + | 0.712933i | \(0.747366\pi\) | |||||||
\(510\) | 2.19615 | 0.0972473 | ||||||||
\(511\) | 49.5692 | 2.19281 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.07180 | −0.223925 | ||||||||
\(514\) | −11.1962 | −0.493841 | ||||||||
\(515\) | −12.0000 | −0.528783 | ||||||||
\(516\) | 6.92820 | 0.304997 | ||||||||
\(517\) | −55.1769 | −2.42668 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.26795 | 0.319028 | ||||||||
\(520\) | −10.3923 | −0.455733 | ||||||||
\(521\) | −26.5359 | −1.16256 | −0.581279 | − | 0.813704i | \(-0.697448\pi\) | ||||
−0.581279 | + | 0.813704i | \(0.697448\pi\) | |||||||
\(522\) | 10.5167 | 0.460302 | ||||||||
\(523\) | −12.5885 | −0.550455 | −0.275227 | − | 0.961379i | \(-0.588753\pi\) | ||||
−0.275227 | + | 0.961379i | \(0.588753\pi\) | |||||||
\(524\) | 8.19615 | 0.358051 | ||||||||
\(525\) | −5.85641 | −0.255595 | ||||||||
\(526\) | 23.3205 | 1.01682 | ||||||||
\(527\) | −2.19615 | −0.0956659 | ||||||||
\(528\) | −3.46410 | −0.150756 | ||||||||
\(529\) | −21.3923 | −0.930100 | ||||||||
\(530\) | 4.39230 | 0.190790 | ||||||||
\(531\) | 6.24871 | 0.271171 | ||||||||
\(532\) | 5.07180 | 0.219890 | ||||||||
\(533\) | −2.78461 | −0.120615 | ||||||||
\(534\) | 3.80385 | 0.164609 | ||||||||
\(535\) | −28.3923 | −1.22751 | ||||||||
\(536\) | 6.19615 | 0.267633 | ||||||||
\(537\) | 8.28719 | 0.357619 | ||||||||
\(538\) | 7.60770 | 0.327991 | ||||||||
\(539\) | −42.5885 | −1.83441 | ||||||||
\(540\) | −6.92820 | −0.298142 | ||||||||
\(541\) | 3.58846 | 0.154280 | 0.0771399 | − | 0.997020i | \(-0.475421\pi\) | ||||
0.0771399 | + | 0.997020i | \(0.475421\pi\) | |||||||
\(542\) | 14.5885 | 0.626628 | ||||||||
\(543\) | −11.2679 | −0.483554 | ||||||||
\(544\) | 1.73205 | 0.0742611 | ||||||||
\(545\) | −13.3923 | −0.573663 | ||||||||
\(546\) | −17.5692 | −0.751893 | ||||||||
\(547\) | 12.5885 | 0.538244 | 0.269122 | − | 0.963106i | \(-0.413267\pi\) | ||||
0.269122 | + | 0.963106i | \(0.413267\pi\) | |||||||
\(548\) | −13.3923 | −0.572091 | ||||||||
\(549\) | −36.1244 | −1.54175 | ||||||||
\(550\) | −9.46410 | −0.403551 | ||||||||
\(551\) | 5.41154 | 0.230539 | ||||||||
\(552\) | −0.928203 | −0.0395070 | ||||||||
\(553\) | 32.7846 | 1.39414 | ||||||||
\(554\) | 6.80385 | 0.289068 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.80385 | −0.0765002 | ||||||||
\(557\) | −10.5167 | −0.445605 | −0.222803 | − | 0.974864i | \(-0.571521\pi\) | ||||
−0.222803 | + | 0.974864i | \(0.571521\pi\) | |||||||
\(558\) | 3.12436 | 0.132265 | ||||||||
\(559\) | 56.7846 | 2.40173 | ||||||||
\(560\) | 6.92820 | 0.292770 | ||||||||
\(561\) | 6.00000 | 0.253320 | ||||||||
\(562\) | 11.1962 | 0.472281 | ||||||||
\(563\) | 11.4115 | 0.480939 | 0.240470 | − | 0.970657i | \(-0.422699\pi\) | ||||
0.240470 | + | 0.970657i | \(0.422699\pi\) | |||||||
\(564\) | 8.53590 | 0.359426 | ||||||||
\(565\) | −34.3923 | −1.44690 | ||||||||
\(566\) | −2.53590 | −0.106592 | ||||||||
\(567\) | 17.8564 | 0.749899 | ||||||||
\(568\) | −2.53590 | −0.106404 | ||||||||
\(569\) | 28.5167 | 1.19548 | 0.597740 | − | 0.801690i | \(-0.296065\pi\) | ||||
0.597740 | + | 0.801690i | \(0.296065\pi\) | |||||||
\(570\) | −1.60770 | −0.0673389 | ||||||||
\(571\) | 14.9808 | 0.626925 | 0.313463 | − | 0.949601i | \(-0.398511\pi\) | ||||
0.313463 | + | 0.949601i | \(0.398511\pi\) | |||||||
\(572\) | −28.3923 | −1.18714 | ||||||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | 1.85641 | 0.0774849 | ||||||||
\(575\) | −2.53590 | −0.105754 | ||||||||
\(576\) | −2.46410 | −0.102671 | ||||||||
\(577\) | 4.14359 | 0.172500 | 0.0862500 | − | 0.996274i | \(-0.472512\pi\) | ||||
0.0862500 | + | 0.996274i | \(0.472512\pi\) | |||||||
\(578\) | 14.0000 | 0.582323 | ||||||||
\(579\) | −8.87564 | −0.368859 | ||||||||
\(580\) | 7.39230 | 0.306949 | ||||||||
\(581\) | 46.6410 | 1.93500 | ||||||||
\(582\) | −3.80385 | −0.157675 | ||||||||
\(583\) | 12.0000 | 0.496989 | ||||||||
\(584\) | −12.3923 | −0.512797 | ||||||||
\(585\) | −25.6077 | −1.05875 | ||||||||
\(586\) | −25.3923 | −1.04895 | ||||||||
\(587\) | 22.0526 | 0.910207 | 0.455103 | − | 0.890439i | \(-0.349602\pi\) | ||||
0.455103 | + | 0.890439i | \(0.349602\pi\) | |||||||
\(588\) | 6.58846 | 0.271703 | ||||||||
\(589\) | 1.60770 | 0.0662439 | ||||||||
\(590\) | 4.39230 | 0.180828 | ||||||||
\(591\) | 19.2679 | 0.792578 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.5359 | 0.966504 | 0.483252 | − | 0.875481i | \(-0.339456\pi\) | ||||
0.483252 | + | 0.875481i | \(0.339456\pi\) | |||||||
\(594\) | −18.9282 | −0.776634 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | 3.92820 | 0.160905 | ||||||||
\(597\) | 3.71281 | 0.151955 | ||||||||
\(598\) | −7.60770 | −0.311102 | ||||||||
\(599\) | 4.73205 | 0.193346 | 0.0966732 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966732 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(600\) | 1.46410 | 0.0597717 | ||||||||
\(601\) | −25.7846 | −1.05178 | −0.525888 | − | 0.850554i | \(-0.676267\pi\) | ||||
−0.525888 | + | 0.850554i | \(0.676267\pi\) | |||||||
\(602\) | −37.8564 | −1.54291 | ||||||||
\(603\) | 15.2679 | 0.621759 | ||||||||
\(604\) | 1.80385 | 0.0733975 | ||||||||
\(605\) | 19.7321 | 0.802222 | ||||||||
\(606\) | −0.339746 | −0.0138012 | ||||||||
\(607\) | −1.94744 | −0.0790442 | −0.0395221 | − | 0.999219i | \(-0.512584\pi\) | ||||
−0.0395221 | + | 0.999219i | \(0.512584\pi\) | |||||||
\(608\) | −1.26795 | −0.0514221 | ||||||||
\(609\) | 12.4974 | 0.506421 | ||||||||
\(610\) | −25.3923 | −1.02810 | ||||||||
\(611\) | 69.9615 | 2.83034 | ||||||||
\(612\) | 4.26795 | 0.172522 | ||||||||
\(613\) | −12.6077 | −0.509220 | −0.254610 | − | 0.967044i | \(-0.581947\pi\) | ||||
−0.254610 | + | 0.967044i | \(0.581947\pi\) | |||||||
\(614\) | −4.00000 | −0.161427 | ||||||||
\(615\) | −0.588457 | −0.0237289 | ||||||||
\(616\) | 18.9282 | 0.762639 | ||||||||
\(617\) | −23.3205 | −0.938848 | −0.469424 | − | 0.882973i | \(-0.655538\pi\) | ||||
−0.469424 | + | 0.882973i | \(0.655538\pi\) | |||||||
\(618\) | 5.07180 | 0.204018 | ||||||||
\(619\) | −21.1769 | −0.851172 | −0.425586 | − | 0.904918i | \(-0.639932\pi\) | ||||
−0.425586 | + | 0.904918i | \(0.639932\pi\) | |||||||
\(620\) | 2.19615 | 0.0881996 | ||||||||
\(621\) | −5.07180 | −0.203524 | ||||||||
\(622\) | 16.3923 | 0.657272 | ||||||||
\(623\) | −20.7846 | −0.832718 | ||||||||
\(624\) | 4.39230 | 0.175833 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −21.5885 | −0.862848 | ||||||||
\(627\) | −4.39230 | −0.175412 | ||||||||
\(628\) | −9.39230 | −0.374794 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 17.0718 | 0.680157 | ||||||||
\(631\) | 29.6603 | 1.18076 | 0.590378 | − | 0.807127i | \(-0.298979\pi\) | ||||
0.590378 | + | 0.807127i | \(0.298979\pi\) | |||||||
\(632\) | −8.19615 | −0.326025 | ||||||||
\(633\) | 9.07180 | 0.360572 | ||||||||
\(634\) | 9.00000 | 0.357436 | ||||||||
\(635\) | −18.3397 | −0.727791 | ||||||||
\(636\) | −1.85641 | −0.0736113 | ||||||||
\(637\) | 54.0000 | 2.13956 | ||||||||
\(638\) | 20.1962 | 0.799573 | ||||||||
\(639\) | −6.24871 | −0.247195 | ||||||||
\(640\) | −1.73205 | −0.0684653 | ||||||||
\(641\) | −19.1436 | −0.756126 | −0.378063 | − | 0.925780i | \(-0.623410\pi\) | ||||
−0.378063 | + | 0.925780i | \(0.623410\pi\) | |||||||
\(642\) | 12.0000 | 0.473602 | ||||||||
\(643\) | −15.1244 | −0.596446 | −0.298223 | − | 0.954496i | \(-0.596394\pi\) | ||||
−0.298223 | + | 0.954496i | \(0.596394\pi\) | |||||||
\(644\) | 5.07180 | 0.199857 | ||||||||
\(645\) | 12.0000 | 0.472500 | ||||||||
\(646\) | 2.19615 | 0.0864065 | ||||||||
\(647\) | 2.53590 | 0.0996965 | 0.0498482 | − | 0.998757i | \(-0.484126\pi\) | ||||
0.0498482 | + | 0.998757i | \(0.484126\pi\) | |||||||
\(648\) | −4.46410 | −0.175366 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | 12.0000 | 0.470679 | ||||||||
\(651\) | 3.71281 | 0.145517 | ||||||||
\(652\) | 2.53590 | 0.0993134 | ||||||||
\(653\) | −17.1962 | −0.672937 | −0.336469 | − | 0.941695i | \(-0.609233\pi\) | ||||
−0.336469 | + | 0.941695i | \(0.609233\pi\) | |||||||
\(654\) | 5.66025 | 0.221333 | ||||||||
\(655\) | 14.1962 | 0.554690 | ||||||||
\(656\) | −0.464102 | −0.0181201 | ||||||||
\(657\) | −30.5359 | −1.19132 | ||||||||
\(658\) | −46.6410 | −1.81826 | ||||||||
\(659\) | −21.4641 | −0.836123 | −0.418061 | − | 0.908419i | \(-0.637290\pi\) | ||||
−0.418061 | + | 0.908419i | \(0.637290\pi\) | |||||||
\(660\) | −6.00000 | −0.233550 | ||||||||
\(661\) | −18.8038 | −0.731385 | −0.365692 | − | 0.930736i | \(-0.619168\pi\) | ||||
−0.365692 | + | 0.930736i | \(0.619168\pi\) | |||||||
\(662\) | 30.9282 | 1.20206 | ||||||||
\(663\) | −7.60770 | −0.295458 | ||||||||
\(664\) | −11.6603 | −0.452506 | ||||||||
\(665\) | 8.78461 | 0.340653 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.41154 | 0.209536 | ||||||||
\(668\) | 6.92820 | 0.268060 | ||||||||
\(669\) | −16.5359 | −0.639315 | ||||||||
\(670\) | 10.7321 | 0.414615 | ||||||||
\(671\) | −69.3731 | −2.67812 | ||||||||
\(672\) | −2.92820 | −0.112958 | ||||||||
\(673\) | 8.39230 | 0.323500 | 0.161750 | − | 0.986832i | \(-0.448286\pi\) | ||||
0.161750 | + | 0.986832i | \(0.448286\pi\) | |||||||
\(674\) | −7.00000 | −0.269630 | ||||||||
\(675\) | 8.00000 | 0.307920 | ||||||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | −34.8564 | −1.33964 | −0.669820 | − | 0.742523i | \(-0.733629\pi\) | ||||
−0.669820 | + | 0.742523i | \(0.733629\pi\) | |||||||
\(678\) | 14.5359 | 0.558248 | ||||||||
\(679\) | 20.7846 | 0.797640 | ||||||||
\(680\) | 3.00000 | 0.115045 | ||||||||
\(681\) | 0.928203 | 0.0355688 | ||||||||
\(682\) | 6.00000 | 0.229752 | ||||||||
\(683\) | −17.0718 | −0.653234 | −0.326617 | − | 0.945157i | \(-0.605909\pi\) | ||||
−0.326617 | + | 0.945157i | \(0.605909\pi\) | |||||||
\(684\) | −3.12436 | −0.119463 | ||||||||
\(685\) | −23.1962 | −0.886279 | ||||||||
\(686\) | −8.00000 | −0.305441 | ||||||||
\(687\) | −13.9090 | −0.530660 | ||||||||
\(688\) | 9.46410 | 0.360815 | ||||||||
\(689\) | −15.2154 | −0.579660 | ||||||||
\(690\) | −1.60770 | −0.0612039 | ||||||||
\(691\) | 22.1962 | 0.844381 | 0.422191 | − | 0.906507i | \(-0.361261\pi\) | ||||
0.422191 | + | 0.906507i | \(0.361261\pi\) | |||||||
\(692\) | 9.92820 | 0.377414 | ||||||||
\(693\) | 46.6410 | 1.77175 | ||||||||
\(694\) | 10.0526 | 0.381590 | ||||||||
\(695\) | −3.12436 | −0.118514 | ||||||||
\(696\) | −3.12436 | −0.118428 | ||||||||
\(697\) | 0.803848 | 0.0304479 | ||||||||
\(698\) | 6.60770 | 0.250105 | ||||||||
\(699\) | 3.37307 | 0.127581 | ||||||||
\(700\) | −8.00000 | −0.302372 | ||||||||
\(701\) | 1.85641 | 0.0701155 | 0.0350578 | − | 0.999385i | \(-0.488838\pi\) | ||||
0.0350578 | + | 0.999385i | \(0.488838\pi\) | |||||||
\(702\) | 24.0000 | 0.905822 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −4.73205 | −0.178346 | ||||||||
\(705\) | 14.7846 | 0.556821 | ||||||||
\(706\) | 30.1244 | 1.13375 | ||||||||
\(707\) | 1.85641 | 0.0698174 | ||||||||
\(708\) | −1.85641 | −0.0697680 | ||||||||
\(709\) | −30.0000 | −1.12667 | −0.563337 | − | 0.826227i | \(-0.690483\pi\) | ||||
−0.563337 | + | 0.826227i | \(0.690483\pi\) | |||||||
\(710\) | −4.39230 | −0.164840 | ||||||||
\(711\) | −20.1962 | −0.757415 | ||||||||
\(712\) | 5.19615 | 0.194734 | ||||||||
\(713\) | 1.60770 | 0.0602087 | ||||||||
\(714\) | 5.07180 | 0.189807 | ||||||||
\(715\) | −49.1769 | −1.83911 | ||||||||
\(716\) | 11.3205 | 0.423067 | ||||||||
\(717\) | −3.71281 | −0.138658 | ||||||||
\(718\) | −33.4641 | −1.24887 | ||||||||
\(719\) | −32.4449 | −1.20999 | −0.604995 | − | 0.796230i | \(-0.706825\pi\) | ||||
−0.604995 | + | 0.796230i | \(0.706825\pi\) | |||||||
\(720\) | −4.26795 | −0.159057 | ||||||||
\(721\) | −27.7128 | −1.03208 | ||||||||
\(722\) | 17.3923 | 0.647275 | ||||||||
\(723\) | 13.1769 | 0.490055 | ||||||||
\(724\) | −15.3923 | −0.572051 | ||||||||
\(725\) | −8.53590 | −0.317015 | ||||||||
\(726\) | −8.33975 | −0.309517 | ||||||||
\(727\) | −1.85641 | −0.0688503 | −0.0344252 | − | 0.999407i | \(-0.510960\pi\) | ||||
−0.0344252 | + | 0.999407i | \(0.510960\pi\) | |||||||
\(728\) | −24.0000 | −0.889499 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | −21.4641 | −0.794422 | ||||||||
\(731\) | −16.3923 | −0.606291 | ||||||||
\(732\) | 10.7321 | 0.396668 | ||||||||
\(733\) | −15.6077 | −0.576483 | −0.288242 | − | 0.957558i | \(-0.593071\pi\) | ||||
−0.288242 | + | 0.957558i | \(0.593071\pi\) | |||||||
\(734\) | −0.392305 | −0.0144802 | ||||||||
\(735\) | 11.4115 | 0.420921 | ||||||||
\(736\) | −1.26795 | −0.0467372 | ||||||||
\(737\) | 29.3205 | 1.08003 | ||||||||
\(738\) | −1.14359 | −0.0420963 | ||||||||
\(739\) | −6.98076 | −0.256791 | −0.128396 | − | 0.991723i | \(-0.540983\pi\) | ||||
−0.128396 | + | 0.991723i | \(0.540983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.56922 | 0.204590 | ||||||||
\(742\) | 10.1436 | 0.372383 | ||||||||
\(743\) | 41.9090 | 1.53749 | 0.768745 | − | 0.639555i | \(-0.220881\pi\) | ||||
0.768745 | + | 0.639555i | \(0.220881\pi\) | |||||||
\(744\) | −0.928203 | −0.0340296 | ||||||||
\(745\) | 6.80385 | 0.249274 | ||||||||
\(746\) | −19.7846 | −0.724366 | ||||||||
\(747\) | −28.7321 | −1.05125 | ||||||||
\(748\) | 8.19615 | 0.299681 | ||||||||
\(749\) | −65.5692 | −2.39585 | ||||||||
\(750\) | 8.87564 | 0.324093 | ||||||||
\(751\) | 36.3923 | 1.32797 | 0.663987 | − | 0.747744i | \(-0.268863\pi\) | ||||
0.663987 | + | 0.747744i | \(0.268863\pi\) | |||||||
\(752\) | 11.6603 | 0.425206 | ||||||||
\(753\) | 3.71281 | 0.135302 | ||||||||
\(754\) | −25.6077 | −0.932577 | ||||||||
\(755\) | 3.12436 | 0.113707 | ||||||||
\(756\) | −16.0000 | −0.581914 | ||||||||
\(757\) | 4.26795 | 0.155121 | 0.0775606 | − | 0.996988i | \(-0.475287\pi\) | ||||
0.0775606 | + | 0.996988i | \(0.475287\pi\) | |||||||
\(758\) | −24.7846 | −0.900218 | ||||||||
\(759\) | −4.39230 | −0.159431 | ||||||||
\(760\) | −2.19615 | −0.0796628 | ||||||||
\(761\) | −32.3205 | −1.17162 | −0.585809 | − | 0.810449i | \(-0.699223\pi\) | ||||
−0.585809 | + | 0.810449i | \(0.699223\pi\) | |||||||
\(762\) | 7.75129 | 0.280800 | ||||||||
\(763\) | −30.9282 | −1.11968 | ||||||||
\(764\) | 24.5885 | 0.889579 | ||||||||
\(765\) | 7.39230 | 0.267269 | ||||||||
\(766\) | 25.8564 | 0.934230 | ||||||||
\(767\) | −15.2154 | −0.549396 | ||||||||
\(768\) | 0.732051 | 0.0264156 | ||||||||
\(769\) | −21.7128 | −0.782984 | −0.391492 | − | 0.920181i | \(-0.628041\pi\) | ||||
−0.391492 | + | 0.920181i | \(0.628041\pi\) | |||||||
\(770\) | 32.7846 | 1.18148 | ||||||||
\(771\) | 8.19615 | 0.295177 | ||||||||
\(772\) | −12.1244 | −0.436365 | ||||||||
\(773\) | −21.9282 | −0.788703 | −0.394351 | − | 0.918960i | \(-0.629031\pi\) | ||||
−0.394351 | + | 0.918960i | \(0.629031\pi\) | |||||||
\(774\) | 23.3205 | 0.838238 | ||||||||
\(775\) | −2.53590 | −0.0910922 | ||||||||
\(776\) | −5.19615 | −0.186531 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.803848 | 0.0288193 | ||||||||
\(779\) | −0.588457 | −0.0210837 | ||||||||
\(780\) | 7.60770 | 0.272399 | ||||||||
\(781\) | −12.0000 | −0.429394 | ||||||||
\(782\) | 2.19615 | 0.0785343 | ||||||||
\(783\) | −17.0718 | −0.610096 | ||||||||
\(784\) | 9.00000 | 0.321429 | ||||||||
\(785\) | −16.2679 | −0.580628 | ||||||||
\(786\) | −6.00000 | −0.214013 | ||||||||
\(787\) | 33.1769 | 1.18263 | 0.591315 | − | 0.806441i | \(-0.298609\pi\) | ||||
0.591315 | + | 0.806441i | \(0.298609\pi\) | |||||||
\(788\) | 26.3205 | 0.937629 | ||||||||
\(789\) | −17.0718 | −0.607772 | ||||||||
\(790\) | −14.1962 | −0.505076 | ||||||||
\(791\) | −79.4256 | −2.82405 | ||||||||
\(792\) | −11.6603 | −0.414329 | ||||||||
\(793\) | 87.9615 | 3.12361 | ||||||||
\(794\) | −5.00000 | −0.177443 | ||||||||
\(795\) | −3.21539 | −0.114038 | ||||||||
\(796\) | 5.07180 | 0.179765 | ||||||||
\(797\) | −20.7846 | −0.736229 | −0.368114 | − | 0.929781i | \(-0.619996\pi\) | ||||
−0.368114 | + | 0.929781i | \(0.619996\pi\) | |||||||
\(798\) | −3.71281 | −0.131432 | ||||||||
\(799\) | −20.1962 | −0.714489 | ||||||||
\(800\) | 2.00000 | 0.0707107 | ||||||||
\(801\) | 12.8038 | 0.452402 | ||||||||
\(802\) | −14.7846 | −0.522063 | ||||||||
\(803\) | −58.6410 | −2.06940 | ||||||||
\(804\) | −4.53590 | −0.159969 | ||||||||
\(805\) | 8.78461 | 0.309617 | ||||||||
\(806\) | −7.60770 | −0.267970 | ||||||||
\(807\) | −5.56922 | −0.196046 | ||||||||
\(808\) | −0.464102 | −0.0163270 | ||||||||
\(809\) | 29.0718 | 1.02211 | 0.511055 | − | 0.859548i | \(-0.329255\pi\) | ||||
0.511055 | + | 0.859548i | \(0.329255\pi\) | |||||||
\(810\) | −7.73205 | −0.271677 | ||||||||
\(811\) | −36.3923 | −1.27791 | −0.638953 | − | 0.769246i | \(-0.720632\pi\) | ||||
−0.638953 | + | 0.769246i | \(0.720632\pi\) | |||||||
\(812\) | 17.0718 | 0.599103 | ||||||||
\(813\) | −10.6795 | −0.374546 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.39230 | 0.153856 | ||||||||
\(816\) | −1.26795 | −0.0443871 | ||||||||
\(817\) | 12.0000 | 0.419827 | ||||||||
\(818\) | −33.5885 | −1.17439 | ||||||||
\(819\) | −59.1384 | −2.06646 | ||||||||
\(820\) | −0.803848 | −0.0280716 | ||||||||
\(821\) | −38.5359 | −1.34491 | −0.672456 | − | 0.740137i | \(-0.734761\pi\) | ||||
−0.672456 | + | 0.740137i | \(0.734761\pi\) | |||||||
\(822\) | 9.80385 | 0.341948 | ||||||||
\(823\) | 38.5885 | 1.34511 | 0.672555 | − | 0.740048i | \(-0.265197\pi\) | ||||
0.672555 | + | 0.740048i | \(0.265197\pi\) | |||||||
\(824\) | 6.92820 | 0.241355 | ||||||||
\(825\) | 6.92820 | 0.241209 | ||||||||
\(826\) | 10.1436 | 0.352941 | ||||||||
\(827\) | −46.6410 | −1.62187 | −0.810934 | − | 0.585138i | \(-0.801040\pi\) | ||||
−0.810934 | + | 0.585138i | \(0.801040\pi\) | |||||||
\(828\) | −3.12436 | −0.108579 | ||||||||
\(829\) | −23.0718 | −0.801317 | −0.400658 | − | 0.916228i | \(-0.631219\pi\) | ||||
−0.400658 | + | 0.916228i | \(0.631219\pi\) | |||||||
\(830\) | −20.1962 | −0.701019 | ||||||||
\(831\) | −4.98076 | −0.172781 | ||||||||
\(832\) | 6.00000 | 0.208013 | ||||||||
\(833\) | −15.5885 | −0.540108 | ||||||||
\(834\) | 1.32051 | 0.0457255 | ||||||||
\(835\) | 12.0000 | 0.415277 | ||||||||
\(836\) | −6.00000 | −0.207514 | ||||||||
\(837\) | −5.07180 | −0.175307 | ||||||||
\(838\) | −10.1436 | −0.350405 | ||||||||
\(839\) | −9.80385 | −0.338466 | −0.169233 | − | 0.985576i | \(-0.554129\pi\) | ||||
−0.169233 | + | 0.985576i | \(0.554129\pi\) | |||||||
\(840\) | −5.07180 | −0.174994 | ||||||||
\(841\) | −10.7846 | −0.371883 | ||||||||
\(842\) | 3.33975 | 0.115095 | ||||||||
\(843\) | −8.19615 | −0.282290 | ||||||||
\(844\) | 12.3923 | 0.426561 | ||||||||
\(845\) | 39.8372 | 1.37044 | ||||||||
\(846\) | 28.7321 | 0.987828 | ||||||||
\(847\) | 45.5692 | 1.56578 | ||||||||
\(848\) | −2.53590 | −0.0870831 | ||||||||
\(849\) | 1.85641 | 0.0637117 | ||||||||
\(850\) | −3.46410 | −0.118818 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 1.85641 | 0.0635994 | ||||||||
\(853\) | 25.7321 | 0.881049 | 0.440524 | − | 0.897741i | \(-0.354793\pi\) | ||||
0.440524 | + | 0.897741i | \(0.354793\pi\) | |||||||
\(854\) | −58.6410 | −2.00665 | ||||||||
\(855\) | −5.41154 | −0.185071 | ||||||||
\(856\) | 16.3923 | 0.560277 | ||||||||
\(857\) | −1.05256 | −0.0359547 | −0.0179774 | − | 0.999838i | \(-0.505723\pi\) | ||||
−0.0179774 | + | 0.999838i | \(0.505723\pi\) | |||||||
\(858\) | 20.7846 | 0.709575 | ||||||||
\(859\) | 14.5359 | 0.495958 | 0.247979 | − | 0.968765i | \(-0.420234\pi\) | ||||
0.247979 | + | 0.968765i | \(0.420234\pi\) | |||||||
\(860\) | 16.3923 | 0.558973 | ||||||||
\(861\) | −1.35898 | −0.0463140 | ||||||||
\(862\) | −22.0526 | −0.751113 | ||||||||
\(863\) | 4.39230 | 0.149516 | 0.0747579 | − | 0.997202i | \(-0.476182\pi\) | ||||
0.0747579 | + | 0.997202i | \(0.476182\pi\) | |||||||
\(864\) | 4.00000 | 0.136083 | ||||||||
\(865\) | 17.1962 | 0.584687 | ||||||||
\(866\) | 12.6077 | 0.428427 | ||||||||
\(867\) | −10.2487 | −0.348064 | ||||||||
\(868\) | 5.07180 | 0.172148 | ||||||||
\(869\) | −38.7846 | −1.31568 | ||||||||
\(870\) | −5.41154 | −0.183468 | ||||||||
\(871\) | −37.1769 | −1.25969 | ||||||||
\(872\) | 7.73205 | 0.261840 | ||||||||
\(873\) | −12.8038 | −0.433345 | ||||||||
\(874\) | −1.60770 | −0.0543811 | ||||||||
\(875\) | −48.4974 | −1.63951 | ||||||||
\(876\) | 9.07180 | 0.306508 | ||||||||
\(877\) | −18.1769 | −0.613791 | −0.306895 | − | 0.951743i | \(-0.599290\pi\) | ||||
−0.306895 | + | 0.951743i | \(0.599290\pi\) | |||||||
\(878\) | −2.53590 | −0.0855824 | ||||||||
\(879\) | 18.5885 | 0.626973 | ||||||||
\(880\) | −8.19615 | −0.276292 | ||||||||
\(881\) | −54.9615 | −1.85170 | −0.925850 | − | 0.377890i | \(-0.876650\pi\) | ||||
−0.925850 | + | 0.377890i | \(0.876650\pi\) | |||||||
\(882\) | 22.1769 | 0.746736 | ||||||||
\(883\) | −18.3397 | −0.617182 | −0.308591 | − | 0.951195i | \(-0.599857\pi\) | ||||
−0.308591 | + | 0.951195i | \(0.599857\pi\) | |||||||
\(884\) | −10.3923 | −0.349531 | ||||||||
\(885\) | −3.21539 | −0.108084 | ||||||||
\(886\) | −9.46410 | −0.317953 | ||||||||
\(887\) | −2.87564 | −0.0965547 | −0.0482773 | − | 0.998834i | \(-0.515373\pi\) | ||||
−0.0482773 | + | 0.998834i | \(0.515373\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42.3538 | −1.42050 | ||||||||
\(890\) | 9.00000 | 0.301681 | ||||||||
\(891\) | −21.1244 | −0.707693 | ||||||||
\(892\) | −22.5885 | −0.756317 | ||||||||
\(893\) | 14.7846 | 0.494748 | ||||||||
\(894\) | −2.87564 | −0.0961759 | ||||||||
\(895\) | 19.6077 | 0.655413 | ||||||||
\(896\) | −4.00000 | −0.133631 | ||||||||
\(897\) | 5.56922 | 0.185951 | ||||||||
\(898\) | 11.0718 | 0.369471 | ||||||||
\(899\) | 5.41154 | 0.180485 | ||||||||
\(900\) | 4.92820 | 0.164273 | ||||||||
\(901\) | 4.39230 | 0.146329 | ||||||||
\(902\) | −2.19615 | −0.0731239 | ||||||||
\(903\) | 27.7128 | 0.922225 | ||||||||
\(904\) | 19.8564 | 0.660414 | ||||||||
\(905\) | −26.6603 | −0.886217 | ||||||||
\(906\) | −1.32051 | −0.0438709 | ||||||||
\(907\) | −40.3013 | −1.33818 | −0.669091 | − | 0.743181i | \(-0.733316\pi\) | ||||
−0.669091 | + | 0.743181i | \(0.733316\pi\) | |||||||
\(908\) | 1.26795 | 0.0420784 | ||||||||
\(909\) | −1.14359 | −0.0379306 | ||||||||
\(910\) | −41.5692 | −1.37801 | ||||||||
\(911\) | 27.1244 | 0.898670 | 0.449335 | − | 0.893363i | \(-0.351661\pi\) | ||||
0.449335 | + | 0.893363i | \(0.351661\pi\) | |||||||
\(912\) | 0.928203 | 0.0307359 | ||||||||
\(913\) | −55.1769 | −1.82609 | ||||||||
\(914\) | 31.9808 | 1.05783 | ||||||||
\(915\) | 18.5885 | 0.614515 | ||||||||
\(916\) | −19.0000 | −0.627778 | ||||||||
\(917\) | 32.7846 | 1.08264 | ||||||||
\(918\) | −6.92820 | −0.228665 | ||||||||
\(919\) | −10.0526 | −0.331603 | −0.165802 | − | 0.986159i | \(-0.553021\pi\) | ||||
−0.165802 | + | 0.986159i | \(0.553021\pi\) | |||||||
\(920\) | −2.19615 | −0.0724050 | ||||||||
\(921\) | 2.92820 | 0.0964876 | ||||||||
\(922\) | 21.7128 | 0.715073 | ||||||||
\(923\) | 15.2154 | 0.500821 | ||||||||
\(924\) | −13.8564 | −0.455842 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21.4641 | 0.705354 | ||||||||
\(927\) | 17.0718 | 0.560711 | ||||||||
\(928\) | −4.26795 | −0.140102 | ||||||||
\(929\) | 16.6077 | 0.544881 | 0.272440 | − | 0.962173i | \(-0.412169\pi\) | ||||
0.272440 | + | 0.962173i | \(0.412169\pi\) | |||||||
\(930\) | −1.60770 | −0.0527184 | ||||||||
\(931\) | 11.4115 | 0.373998 | ||||||||
\(932\) | 4.60770 | 0.150930 | ||||||||
\(933\) | −12.0000 | −0.392862 | ||||||||
\(934\) | 18.2487 | 0.597116 | ||||||||
\(935\) | 14.1962 | 0.464264 | ||||||||
\(936\) | 14.7846 | 0.483250 | ||||||||
\(937\) | −26.1769 | −0.855163 | −0.427581 | − | 0.903977i | \(-0.640634\pi\) | ||||
−0.427581 | + | 0.903977i | \(0.640634\pi\) | |||||||
\(938\) | 24.7846 | 0.809246 | ||||||||
\(939\) | 15.8038 | 0.515739 | ||||||||
\(940\) | 20.1962 | 0.658726 | ||||||||
\(941\) | 18.2154 | 0.593805 | 0.296902 | − | 0.954908i | \(-0.404046\pi\) | ||||
0.296902 | + | 0.954908i | \(0.404046\pi\) | |||||||
\(942\) | 6.87564 | 0.224021 | ||||||||
\(943\) | −0.588457 | −0.0191628 | ||||||||
\(944\) | −2.53590 | −0.0825365 | ||||||||
\(945\) | −27.7128 | −0.901498 | ||||||||
\(946\) | 44.7846 | 1.45607 | ||||||||
\(947\) | 31.6077 | 1.02711 | 0.513556 | − | 0.858056i | \(-0.328328\pi\) | ||||
0.513556 | + | 0.858056i | \(0.328328\pi\) | |||||||
\(948\) | 6.00000 | 0.194871 | ||||||||
\(949\) | 74.3538 | 2.41363 | ||||||||
\(950\) | 2.53590 | 0.0822754 | ||||||||
\(951\) | −6.58846 | −0.213645 | ||||||||
\(952\) | 6.92820 | 0.224544 | ||||||||
\(953\) | 19.8564 | 0.643212 | 0.321606 | − | 0.946874i | \(-0.395777\pi\) | ||||
0.321606 | + | 0.946874i | \(0.395777\pi\) | |||||||
\(954\) | −6.24871 | −0.202309 | ||||||||
\(955\) | 42.5885 | 1.37813 | ||||||||
\(956\) | −5.07180 | −0.164034 | ||||||||
\(957\) | −14.7846 | −0.477919 | ||||||||
\(958\) | −2.53590 | −0.0819312 | ||||||||
\(959\) | −53.5692 | −1.72984 | ||||||||
\(960\) | 1.26795 | 0.0409229 | ||||||||
\(961\) | −29.3923 | −0.948139 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.3923 | 1.30162 | ||||||||
\(964\) | 18.0000 | 0.579741 | ||||||||
\(965\) | −21.0000 | −0.676014 | ||||||||
\(966\) | −3.71281 | −0.119458 | ||||||||
\(967\) | 58.6410 | 1.88577 | 0.942884 | − | 0.333121i | \(-0.108102\pi\) | ||||
0.942884 | + | 0.333121i | \(0.108102\pi\) | |||||||
\(968\) | −11.3923 | −0.366163 | ||||||||
\(969\) | −1.60770 | −0.0516466 | ||||||||
\(970\) | −9.00000 | −0.288973 | ||||||||
\(971\) | 18.5885 | 0.596532 | 0.298266 | − | 0.954483i | \(-0.403592\pi\) | ||||
0.298266 | + | 0.954483i | \(0.403592\pi\) | |||||||
\(972\) | 15.2679 | 0.489720 | ||||||||
\(973\) | −7.21539 | −0.231315 | ||||||||
\(974\) | 10.0526 | 0.322105 | ||||||||
\(975\) | −8.78461 | −0.281333 | ||||||||
\(976\) | 14.6603 | 0.469263 | ||||||||
\(977\) | −2.28719 | −0.0731736 | −0.0365868 | − | 0.999330i | \(-0.511649\pi\) | ||||
−0.0365868 | + | 0.999330i | \(0.511649\pi\) | |||||||
\(978\) | −1.85641 | −0.0593613 | ||||||||
\(979\) | 24.5885 | 0.785851 | ||||||||
\(980\) | 15.5885 | 0.497955 | ||||||||
\(981\) | 19.0526 | 0.608301 | ||||||||
\(982\) | 22.9808 | 0.733346 | ||||||||
\(983\) | 25.5167 | 0.813855 | 0.406928 | − | 0.913460i | \(-0.366600\pi\) | ||||
0.406928 | + | 0.913460i | \(0.366600\pi\) | |||||||
\(984\) | 0.339746 | 0.0108307 | ||||||||
\(985\) | 45.5885 | 1.45257 | ||||||||
\(986\) | 7.39230 | 0.235419 | ||||||||
\(987\) | 34.1436 | 1.08680 | ||||||||
\(988\) | 7.60770 | 0.242033 | ||||||||
\(989\) | 12.0000 | 0.381578 | ||||||||
\(990\) | −20.1962 | −0.641876 | ||||||||
\(991\) | 32.1051 | 1.01985 | 0.509926 | − | 0.860218i | \(-0.329673\pi\) | ||||
0.509926 | + | 0.860218i | \(0.329673\pi\) | |||||||
\(992\) | −1.26795 | −0.0402574 | ||||||||
\(993\) | −22.6410 | −0.718491 | ||||||||
\(994\) | −10.1436 | −0.321735 | ||||||||
\(995\) | 8.78461 | 0.278491 | ||||||||
\(996\) | 8.53590 | 0.270470 | ||||||||
\(997\) | −59.5692 | −1.88658 | −0.943288 | − | 0.331975i | \(-0.892285\pi\) | ||||
−0.943288 | + | 0.331975i | \(0.892285\pi\) | |||||||
\(998\) | −8.19615 | −0.259445 | ||||||||
\(999\) | 0 | 0 |
(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 | 2738.2.a.f.1.2 | 2 | ||
37.23 | odd | 12 | 74.2.e.a.11.2 | ✓ | 4 | ||
37.29 | odd | 12 | 74.2.e.a.27.2 | yes | 4 | ||
37.36 | even | 2 | 2738.2.a.j.1.2 | 2 | |||
111.23 | even | 12 | 666.2.s.e.307.1 | 4 | |||
111.29 | even | 12 | 666.2.s.e.397.1 | 4 | |||
148.23 | even | 12 | 592.2.w.d.529.1 | 4 | |||
148.103 | even | 12 | 592.2.w.d.545.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.e.a.11.2 | ✓ | 4 | 37.23 | odd | 12 | ||
74.2.e.a.27.2 | yes | 4 | 37.29 | odd | 12 | ||
592.2.w.d.529.1 | 4 | 148.23 | even | 12 | |||
592.2.w.d.545.1 | 4 | 148.103 | even | 12 | |||
666.2.s.e.307.1 | 4 | 111.23 | even | 12 | |||
666.2.s.e.397.1 | 4 | 111.29 | even | 12 | |||
2738.2.a.f.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2738.2.a.j.1.2 | 2 | 37.36 | even | 2 |