Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.527896576.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 2x^{5} + 7x^{4} - 10x^{3} + 8x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 115) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.5 | ||
Root | \(0.790245 - 0.790245i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.d.369.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.580491i | 0.335147i | 0.985860 | + | 0.167573i | \(0.0535931\pi\) | ||||
−0.985860 | + | 0.167573i | \(0.946407\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.209755 | − | 2.22621i | −0.0938051 | − | 0.995591i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.315061i | 0.119082i | 0.998226 | + | 0.0595410i | \(0.0189637\pi\) | ||||
−0.998226 | + | 0.0595410i | \(0.981036\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.66303 | 0.887677 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.34797 | 1.31096 | 0.655481 | − | 0.755212i | \(-0.272466\pi\) | ||||
0.655481 | + | 0.755212i | \(0.272466\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.58049i | 1.27040i | 0.772348 | + | 0.635200i | \(0.219082\pi\) | ||||
−0.772348 | + | 0.635200i | \(0.780918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.29229 | − | 0.121761i | 0.333669 | − | 0.0314385i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.917461i | − | 0.222517i | −0.993792 | − | 0.111258i | \(-0.964512\pi\) | ||
0.993792 | − | 0.111258i | \(-0.0354881\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.76748 | 0.634903 | 0.317451 | − | 0.948275i | \(-0.397173\pi\) | ||||
0.317451 | + | 0.948275i | \(0.397173\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.182890 | −0.0399099 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.91201 | + | 0.933914i | −0.982401 | + | 0.186783i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.28734i | 0.632648i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.03291 | −1.30598 | −0.652989 | − | 0.757367i | \(-0.726485\pi\) | ||||
−0.652989 | + | 0.757367i | \(0.726485\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.867829 | 0.155867 | 0.0779333 | − | 0.996959i | \(-0.475168\pi\) | ||||
0.0779333 | + | 0.996959i | \(0.475168\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.52396i | 0.439364i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.701392 | − | 0.0660856i | 0.118557 | − | 0.0111705i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.68904i | − | 0.770873i | −0.922734 | − | 0.385436i | \(-0.874051\pi\) | ||
0.922734 | − | 0.385436i | \(-0.125949\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.65893 | −0.425770 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.69184 | 0.732742 | 0.366371 | − | 0.930469i | \(-0.380600\pi\) | ||||
0.366371 | + | 0.930469i | \(0.380600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.08944i | − | 1.38613i | −0.720877 | − | 0.693063i | \(-0.756261\pi\) | ||
0.720877 | − | 0.693063i | \(-0.243739\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.558583 | − | 5.92846i | −0.0832686 | − | 0.883763i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.24762i | 1.20304i | 0.798858 | + | 0.601519i | \(0.205438\pi\) | ||||
−0.798858 | + | 0.601519i | \(0.794562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.90074 | 0.985819 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.532578 | 0.0745758 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.9048i | 1.49789i | 0.662630 | + | 0.748947i | \(0.269440\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.912006 | − | 9.67948i | −0.122975 | − | 1.30518i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.60650i | 0.212786i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50205 | 0.195550 | 0.0977750 | − | 0.995209i | \(-0.468827\pi\) | ||||
0.0977750 | + | 0.995209i | \(0.468827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4634 | 1.46774 | 0.733870 | − | 0.679290i | \(-0.237712\pi\) | ||||
0.733870 | + | 0.679290i | \(0.237712\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.839018i | 0.105706i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.1971 | − | 0.960779i | 1.26480 | − | 0.119170i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.68494i | − | 0.205848i | −0.994689 | − | 0.102924i | \(-0.967180\pi\) | ||
0.994689 | − | 0.102924i | \(-0.0328198\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.580491 | −0.0698829 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.36578 | 0.636801 | 0.318401 | − | 0.947956i | \(-0.396854\pi\) | ||||
0.318401 | + | 0.947956i | \(0.396854\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.1484i | − | 1.18778i | −0.804548 | − | 0.593888i | \(-0.797592\pi\) | ||
0.804548 | − | 0.593888i | \(-0.202408\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.542129 | − | 2.85138i | −0.0625997 | − | 0.329248i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.36988i | 0.156112i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.39760 | 0.832295 | 0.416148 | − | 0.909297i | \(-0.363380\pi\) | ||||
0.416148 | + | 0.909297i | \(0.363380\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.08082 | 0.675647 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.3052i | 1.67997i | 0.542611 | + | 0.839984i | \(0.317436\pi\) | ||||
−0.542611 | + | 0.839984i | \(0.682564\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.04246 | + | 0.192442i | −0.221536 | + | 0.0208732i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4.08254i | − | 0.437694i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.9326 | 1.15885 | 0.579424 | − | 0.815026i | \(-0.303277\pi\) | ||||
0.579424 | + | 0.815026i | \(0.303277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.44314 | −0.151282 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.503767i | 0.0522382i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.580491 | − | 6.16098i | −0.0595571 | − | 0.632103i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.2158i | − | 1.44340i | −0.692208 | − | 0.721698i | \(-0.743362\pi\) | ||
0.692208 | − | 0.721698i | \(-0.256638\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.5788 | 1.16371 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.16508 | −0.812456 | −0.406228 | − | 0.913772i | \(-0.633156\pi\) | ||||
−0.406228 | + | 0.913772i | \(0.633156\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.287338i | − | 0.0283122i | −0.999900 | − | 0.0141561i | \(-0.995494\pi\) | ||
0.999900 | − | 0.0141561i | \(-0.00450618\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0383621 | + | 0.407152i | 0.00374375 | + | 0.0397340i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 14.0935i | − | 1.36247i | −0.732063 | − | 0.681237i | \(-0.761442\pi\) | ||
0.732063 | − | 0.681237i | \(-0.238558\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.76338 | −0.168901 | −0.0844506 | − | 0.996428i | \(-0.526914\pi\) | ||||
−0.0844506 | + | 0.996428i | \(0.526914\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.72194 | 0.258355 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.315061i | − | 0.0296385i | −0.999890 | − | 0.0148192i | \(-0.995283\pi\) | ||
0.999890 | − | 0.0148192i | \(-0.00471728\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.22621 | − | 0.209755i | 0.207595 | − | 0.0195597i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.1980i | 1.12770i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.289056 | 0.0264978 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.90483 | 0.718621 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.72357i | 0.245576i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.10940 | + | 10.7393i | 0.278114 | + | 0.960548i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.3284i | 1.89259i | 0.323300 | + | 0.946296i | \(0.395208\pi\) | ||||
−0.323300 | + | 0.946296i | \(0.604792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.27634 | 0.464556 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.11373 | −0.708900 | −0.354450 | − | 0.935075i | \(-0.615332\pi\) | ||||
−0.354450 | + | 0.935075i | \(0.615332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.871925i | 0.0756055i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.31830 | − | 0.689534i | 0.629859 | − | 0.0593456i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.22680i | − | 0.617427i | −0.951155 | − | 0.308713i | \(-0.900102\pi\) | ||
0.951155 | − | 0.308713i | \(-0.0998984\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8431 | −0.919701 | −0.459850 | − | 0.887996i | \(-0.652097\pi\) | ||||
−0.459850 | + | 0.887996i | \(0.652097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.78767 | −0.403194 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.9158i | 1.66545i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.47518 | + | 15.6567i | 0.122507 | + | 1.30022i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.00582i | 0.330394i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.90074 | 0.647254 | 0.323627 | − | 0.946185i | \(-0.395098\pi\) | ||||
0.323627 | + | 0.946185i | \(0.395098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.03700 | 0.654042 | 0.327021 | − | 0.945017i | \(-0.393955\pi\) | ||||
0.327021 | + | 0.945017i | \(0.393955\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.44323i | − | 0.197523i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.182031 | − | 1.93197i | −0.0146211 | − | 0.155179i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.75928i | − | 0.379832i | −0.981800 | − | 0.189916i | \(-0.939178\pi\) | ||
0.981800 | − | 0.189916i | \(-0.0608216\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.33016 | −0.502014 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.315061 | −0.0248303 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.11545i | − | 0.165695i | −0.996562 | − | 0.0828473i | \(-0.973599\pi\) | ||
0.996562 | − | 0.0828473i | \(-0.0264014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.61885 | − | 0.529411i | 0.437427 | − | 0.0412146i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 15.8760i | − | 1.22852i | −0.789102 | − | 0.614262i | \(-0.789454\pi\) | ||
0.789102 | − | 0.614262i | \(-0.210546\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.98090 | −0.613915 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.36988 | 0.563589 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 0.0767241i | − | 0.00583323i | −0.999996 | − | 0.00291661i | \(-0.999072\pi\) | ||
0.999996 | − | 0.00291661i | \(-0.000928388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.294240 | − | 1.54758i | −0.0222425 | − | 0.116986i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.871925i | 0.0655379i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.7247 | −1.54904 | −0.774520 | − | 0.632549i | \(-0.782009\pi\) | ||||
−0.774520 | + | 0.632549i | \(0.782009\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.5610 | −0.859319 | −0.429660 | − | 0.902991i | \(-0.641366\pi\) | ||||
−0.429660 | + | 0.902991i | \(0.641366\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.65441i | 0.491908i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.4388 | + | 0.983546i | −0.767474 | + | 0.0723118i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.98909i | − | 0.291711i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.03571 | −0.0753371 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.9683 | −1.58957 | −0.794784 | − | 0.606892i | \(-0.792416\pi\) | ||||
−0.794784 | + | 0.606892i | \(0.792416\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.2914i | 1.46061i | 0.683122 | + | 0.730305i | \(0.260622\pi\) | ||||
−0.683122 | + | 0.730305i | \(0.739378\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.557723 | + | 5.91934i | 0.0399394 | + | 0.423893i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.62159i | − | 0.614263i | −0.951667 | − | 0.307131i | \(-0.900631\pi\) | ||
0.951667 | − | 0.307131i | \(-0.0993691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.7796 | 1.47302 | 0.736512 | − | 0.676424i | \(-0.236471\pi\) | ||||
0.736512 | + | 0.676424i | \(0.236471\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.978092 | 0.0689893 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2.21580i | − | 0.155519i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.984135 | − | 10.4450i | −0.0687350 | − | 0.729512i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.66303i | 0.185093i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0329 | 0.832334 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.16508 | 0.286736 | 0.143368 | − | 0.989669i | \(-0.454207\pi\) | ||||
0.143368 | + | 0.989669i | \(0.454207\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.11479i | 0.213422i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.2350 | + | 1.90655i | −1.38001 | + | 0.130026i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.273419i | 0.0185609i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.89103 | 0.398079 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.20242 | 0.282685 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.7618i | − | 1.25638i | −0.778060 | − | 0.628190i | \(-0.783796\pi\) | ||
0.778060 | − | 0.628190i | \(-0.216204\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0808 | + | 2.48704i | −0.872055 | + | 0.165803i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 10.9637i | − | 0.727689i | −0.931460 | − | 0.363845i | \(-0.881464\pi\) | ||
0.931460 | − | 0.363845i | \(-0.118536\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.9367 | −1.71394 | −0.856971 | − | 0.515364i | \(-0.827657\pi\) | ||||
−0.856971 | + | 0.515364i | \(0.827657\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.795201 | −0.0523204 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.23942i | 0.539783i | 0.962891 | + | 0.269891i | \(0.0869878\pi\) | ||||
−0.962891 | + | 0.269891i | \(0.913012\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.3609 | − | 1.72998i | 1.19773 | − | 0.112851i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.29424i | 0.278941i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0508 | 1.03824 | 0.519120 | − | 0.854701i | \(-0.326260\pi\) | ||||
0.519120 | + | 0.854701i | \(0.326260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.09755 | −0.135115 | −0.0675574 | − | 0.997715i | \(-0.521521\pi\) | ||||
−0.0675574 | + | 0.997715i | \(0.521521\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.3919i | 0.859089i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.44746 | − | 15.3625i | −0.0924749 | − | 0.981473i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.6764i | 0.806580i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.88455 | −0.563036 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.7018 | 0.864847 | 0.432423 | − | 0.901671i | \(-0.357659\pi\) | ||||
0.432423 | + | 0.901671i | \(0.357659\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.34797i | 0.273354i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.111711 | − | 1.18563i | −0.00699559 | − | 0.0742470i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.998281i | 0.0622711i | 0.999515 | + | 0.0311355i | \(0.00991235\pi\) | ||||
−0.999515 | + | 0.0311355i | \(0.990088\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.47733 | 0.0917971 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.7288 | −1.15929 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 9.18527i | − | 0.566388i | −0.959063 | − | 0.283194i | \(-0.908606\pi\) | ||
0.959063 | − | 0.283194i | \(-0.0913940\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.2764 | − | 2.28734i | 1.49129 | − | 0.140510i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.34625i | 0.388384i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.4398 | −1.30721 | −0.653603 | − | 0.756837i | \(-0.726744\pi\) | ||||
−0.653603 | + | 0.756837i | \(0.726744\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.2488 | 1.53376 | 0.766878 | − | 0.641793i | \(-0.221809\pi\) | ||||
0.766878 | + | 0.641793i | \(0.221809\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.837727i | − | 0.0507016i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.3572 | + | 4.06063i | −1.28789 | + | 0.244865i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 30.8114i | − | 1.85128i | −0.378409 | − | 0.925638i | \(-0.623529\pi\) | ||
0.378409 | − | 0.925638i | \(-0.376471\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.31105 | 0.138359 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.60821 | 0.215248 | 0.107624 | − | 0.994192i | \(-0.465676\pi\) | ||||
0.107624 | + | 0.994192i | \(0.465676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.23942i | 0.311451i | 0.987800 | + | 0.155726i | \(0.0497716\pi\) | ||||
−0.987800 | + | 0.155726i | \(0.950228\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.57639 | − | 0.336970i | 0.211847 | − | 0.0199604i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.47822i | 0.0872565i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.1583 | 0.950486 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.25214 | 0.483749 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.90074i | 0.111042i | 0.998458 | + | 0.0555211i | \(0.0176820\pi\) | ||||
−0.998458 | + | 0.0555211i | \(0.982318\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.315061 | − | 3.34387i | −0.0183436 | − | 0.194688i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.2932i | 0.829378i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.58049 | −0.264897 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.86373 | 0.165063 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.73975i | − | 0.272292i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.40450 | − | 25.5199i | −0.137681 | − | 1.46127i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.82467i | 0.161213i | 0.996746 | + | 0.0806063i | \(0.0256856\pi\) | ||||
−0.996746 | + | 0.0806063i | \(0.974314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.166797 | 0.00948875 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.1028 | −0.913107 | −0.456554 | − | 0.889696i | \(-0.650916\pi\) | ||||
−0.456554 | + | 0.889696i | \(0.650916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.3740i | 1.49075i | 0.666648 | + | 0.745373i | \(0.267728\pi\) | ||||
−0.666648 | + | 0.745373i | \(0.732272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.86783 | − | 0.175988i | 0.105240 | − | 0.00991579i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.5020i | 0.870682i | 0.900266 | + | 0.435341i | \(0.143372\pi\) | ||||
−0.900266 | + | 0.435341i | \(0.856628\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.5789 | −1.71209 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.18117 | 0.456628 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.53905i | − | 0.141277i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.27779 | − | 22.4994i | −0.237289 | − | 1.24804i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.02363i | − | 0.0566067i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.59851 | −0.143260 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.0302 | −1.04599 | −0.522997 | − | 0.852335i | \(-0.675186\pi\) | ||||
−0.522997 | + | 0.852335i | \(0.675186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 12.4870i | − | 0.684286i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.75102 | + | 0.353423i | −0.204940 | + | 0.0193096i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.09354i | 0.222989i | 0.993765 | + | 0.111495i | \(0.0355638\pi\) | ||||
−0.993765 | + | 0.111495i | \(0.964436\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.182890 | 0.00993324 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.77329 | 0.204335 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.37959i | 0.236475i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.121761 | + | 1.29229i | 0.00655537 | + | 0.0695748i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 17.4357i | − | 0.935997i | −0.883729 | − | 0.467998i | \(-0.844975\pi\) | ||
0.883729 | − | 0.467998i | \(-0.155025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.48770 | −0.454336 | −0.227168 | − | 0.973856i | \(-0.572947\pi\) | ||||
−0.227168 | + | 0.973856i | \(0.572947\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.0576 | −0.803716 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.5696i | 1.09481i | 0.836868 | + | 0.547404i | \(0.184384\pi\) | ||||
−0.836868 | + | 0.547404i | \(0.815616\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.12550 | − | 11.9453i | −0.0597352 | − | 0.633993i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.167795i | 0.00888064i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.4121 | −1.18286 | −0.591432 | − | 0.806355i | \(-0.701437\pi\) | ||||
−0.591432 | + | 0.806355i | \(0.701437\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3411 | −0.596898 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.58868i | 0.240843i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.5923 | + | 2.12866i | −1.18254 | + | 0.111419i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 21.9401i | − | 1.14526i | −0.819812 | − | 0.572632i | \(-0.805922\pi\) | ||
0.819812 | − | 0.572632i | \(-0.194078\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.4945 | 0.650438 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.43569 | −0.178372 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.853821i | 0.0442092i | 0.999756 | + | 0.0221046i | \(0.00703668\pi\) | ||||
−0.999756 | + | 0.0221046i | \(0.992963\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.23404 | + | 1.80498i | −0.321924 | + | 0.0932088i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 32.2142i | − | 1.65911i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.52049 | −0.129469 | −0.0647345 | − | 0.997903i | \(-0.520620\pi\) | ||||
−0.0647345 | + | 0.997903i | \(0.520620\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.3810 | −0.634296 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.5983i | 0.694841i | 0.937709 | + | 0.347420i | \(0.112942\pi\) | ||||
−0.937709 | + | 0.347420i | \(0.887058\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.04963 | − | 0.287338i | 0.155424 | − | 0.0146441i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 24.2055i | − | 1.23043i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.7398 | −0.544527 | −0.272264 | − | 0.962223i | \(-0.587772\pi\) | ||||
−0.272264 | + | 0.962223i | \(0.587772\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.917461 | 0.0463980 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.70995i | − | 0.237585i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.55168 | − | 16.4686i | −0.0780735 | − | 0.828625i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 19.5868i | − | 0.983031i | −0.870869 | − | 0.491516i | \(-0.836443\pi\) | ||
0.870869 | − | 0.491516i | \(-0.163557\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.506145 | −0.0253389 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.01209 | −0.400105 | −0.200052 | − | 0.979785i | \(-0.564111\pi\) | ||||
−0.200052 | + | 0.979785i | \(0.564111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.97508i | 0.198013i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.27548 | − | 13.5372i | −0.0633791 | − | 0.672668i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 20.3878i | − | 1.01058i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.2350 | 1.39613 | 0.698065 | − | 0.716034i | \(-0.254045\pi\) | ||||
0.698065 | + | 0.716034i | \(0.254045\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.19509 | 0.206929 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.473237i | 0.0232865i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.0726 | − | 3.21034i | 1.67256 | − | 0.157590i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 6.29433i | − | 0.308235i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.9470 | −1.07218 | −0.536091 | − | 0.844160i | \(-0.680100\pi\) | ||||
−0.536091 | + | 0.844160i | \(0.680100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.747198 | 0.0364162 | 0.0182081 | − | 0.999834i | \(-0.494204\pi\) | ||||
0.0182081 | + | 0.999834i | \(0.494204\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.9637i | 1.06791i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.856830 | + | 4.50657i | 0.0415624 | + | 0.218601i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.61168i | 0.174781i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.5610 | −0.558168 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.3642 | −1.31808 | −0.659042 | − | 0.752106i | \(-0.729038\pi\) | ||||
−0.659042 | + | 0.752106i | \(0.729038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.4265i | 1.22192i | 0.791662 | + | 0.610960i | \(0.209216\pi\) | ||||
−0.791662 | + | 0.610960i | \(0.790784\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.08858 | + | 0.856331i | −0.435764 | + | 0.0410579i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.76748i | 0.132386i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.8097 | −1.47047 | −0.735233 | − | 0.677815i | \(-0.762927\pi\) | ||||
−0.735233 | + | 0.677815i | \(0.762927\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.3769 | 0.875089 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.5778i | 1.16773i | 0.811852 | + | 0.583863i | \(0.198459\pi\) | ||||
−0.811852 | + | 0.583863i | \(0.801541\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.29315 | − | 24.3381i | −0.108706 | − | 1.15374i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.58631i | 0.216925i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.6816 | −1.82550 | −0.912749 | − | 0.408522i | \(-0.866044\pi\) | ||||
−0.912749 | + | 0.408522i | \(0.866044\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.4000 | 0.960597 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.66541i | 0.219200i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.302704 | + | 3.21272i | 0.0141910 | + | 0.150615i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.40041i | 0.299398i | 0.988732 | + | 0.149699i | \(0.0478305\pi\) | ||||
−0.988732 | + | 0.149699i | \(0.952169\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.01600 | 0.140775 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.8337 | −1.11005 | −0.555024 | − | 0.831835i | \(-0.687291\pi\) | ||||
−0.555024 | + | 0.831835i | \(0.687291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.5529i | 1.23402i | 0.786957 | + | 0.617008i | \(0.211655\pi\) | ||||
−0.786957 | + | 0.617008i | \(0.788345\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.12149 | − | 0.105667i | 0.0520078 | − | 0.00490021i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.6049i | 0.860931i | 0.902607 | + | 0.430465i | \(0.141651\pi\) | ||||
−0.902607 | + | 0.430465i | \(0.858349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.530859 | 0.0245128 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.76272 | 0.127300 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 39.5206i | − | 1.81716i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.5939 | + | 2.58459i | −0.623729 | + | 0.118589i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.0399i | 1.32965i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.9627 | 1.36903 | 0.684514 | − | 0.728999i | \(-0.260014\pi\) | ||||
0.684514 | + | 0.728999i | \(0.260014\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.4781 | 0.979316 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.182890i | − | 0.00832180i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.6473 | + | 2.98183i | −1.43703 | + | 0.135398i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 37.2265i | − | 1.68689i | −0.537214 | − | 0.843446i | \(-0.680523\pi\) | ||
0.537214 | − | 0.843446i | \(-0.319477\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.22800 | 0.0555320 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.691841 | 0.0312224 | 0.0156112 | − | 0.999878i | \(-0.495031\pi\) | ||||
0.0156112 | + | 0.999878i | \(0.495031\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.45242i | 0.290602i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.42870 | − | 25.7768i | −0.109162 | − | 1.15858i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.69055i | 0.0758315i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.7988 | −1.11014 | −0.555072 | − | 0.831802i | \(-0.687309\pi\) | ||||
−0.555072 | + | 0.831802i | \(0.687309\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.21589 | 0.411735 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 22.6049i | − | 1.00790i | −0.863732 | − | 0.503951i | \(-0.831879\pi\) | ||
0.863732 | − | 0.503951i | \(-0.168121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.71266 | + | 18.1772i | 0.0762125 | + | 0.808873i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4.63284i | − | 0.205752i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.1240 | 0.847655 | 0.423828 | − | 0.905743i | \(-0.360686\pi\) | ||||
0.423828 | + | 0.905743i | \(0.360686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.19735 | 0.141443 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.09763i | 0.401670i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.639674 | + | 0.0602704i | −0.0281874 | + | 0.00265583i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.8604i | 1.57714i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.0445377 | 0.00195499 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.8425 | 0.562638 | 0.281319 | − | 0.959614i | \(-0.409228\pi\) | ||||
0.281319 | + | 0.959614i | \(0.409228\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.8289i | 1.43551i | 0.696298 | + | 0.717753i | \(0.254829\pi\) | ||||
−0.696298 | + | 0.717753i | \(0.745171\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.898358 | − | 0.170804i | 0.0392076 | − | 0.00745449i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 0.796199i | − | 0.0346830i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.4909i | 0.930876i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −31.3752 | + | 2.95618i | −1.35647 | + | 0.127807i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 12.0305i | − | 0.519156i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.0042 | 1.29237 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.7261 | −1.10605 | −0.553026 | − | 0.833164i | \(-0.686527\pi\) | ||||
−0.553026 | + | 0.833164i | \(0.686527\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 6.71103i | − | 0.287998i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.369877 | + | 3.92565i | 0.0158438 | + | 0.168157i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.0191i | 1.54006i | 0.638005 | + | 0.770032i | \(0.279760\pi\) | ||||
−0.638005 | + | 0.770032i | \(0.720240\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.5274 | 1.30288 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.4634 | −0.829169 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.33070i | 0.0991114i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.570940 | − | 6.05961i | −0.0242350 | − | 0.257216i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.2148i | 1.53447i | 0.641366 | + | 0.767235i | \(0.278368\pi\) | ||||
−0.641366 | + | 0.767235i | \(0.721632\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.6341 | 1.76094 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.31563 | 0.0977660 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.3308i | 0.983277i | 0.870799 | + | 0.491638i | \(0.163602\pi\) | ||||
−0.870799 | + | 0.491638i | \(0.836398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.701392 | + | 0.0660856i | −0.0295078 | + | 0.00278024i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.91583i | 0.0804574i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.6845 | −0.657529 | −0.328764 | − | 0.944412i | \(-0.606632\pi\) | ||||
−0.328764 | + | 0.944412i | \(0.606632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.7600 | −1.62206 | −0.811028 | − | 0.585007i | \(-0.801092\pi\) | ||||
−0.811028 | + | 0.585007i | \(0.801092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 12.7524i | − | 0.532738i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.933914 | − | 4.91201i | −0.0389469 | − | 0.204845i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21.5902i | − | 0.898812i | −0.893328 | − | 0.449406i | \(-0.851636\pi\) | ||
0.893328 | − | 0.449406i | \(-0.148364\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.7790 | −0.489518 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.82209 | −0.200054 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 47.4139i | 1.96368i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.1553 | − | 2.55858i | 1.12273 | − | 0.105784i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 24.3902i | − | 1.00669i | −0.864086 | − | 0.503345i | \(-0.832103\pi\) | ||
0.864086 | − | 0.503345i | \(-0.167897\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.40170 | 0.0989602 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.00476 | 0.205868 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.9747i | 0.573874i | 0.957949 | + | 0.286937i | \(0.0926370\pi\) | ||||
−0.957949 | + | 0.286937i | \(0.907363\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0606309 | − | 0.643500i | −0.00248562 | − | 0.0263809i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.0623i | 0.493679i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.9932 | −0.857758 | −0.428879 | − | 0.903362i | \(-0.641091\pi\) | ||||
−0.428879 | + | 0.903362i | \(0.641091\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.3007 | −0.542546 | −0.271273 | − | 0.962502i | \(-0.587445\pi\) | ||||
−0.271273 | + | 0.962502i | \(0.587445\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.48704i | − | 0.182726i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.65807 | − | 17.5978i | −0.0674103 | − | 0.715452i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.3549i | 0.501469i | 0.968056 | + | 0.250734i | \(0.0806721\pi\) | ||||
−0.968056 | + | 0.250734i | \(0.919328\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.28625 | 0.0521215 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.7781 | −1.52834 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.6291i | 0.590865i | 0.955364 | + | 0.295432i | \(0.0954637\pi\) | ||||
−0.955364 | + | 0.295432i | \(0.904536\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.06324 | − | 0.571281i | 0.244493 | − | 0.0230363i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.3723i | 0.699384i | 0.936865 | + | 0.349692i | \(0.113714\pi\) | ||||
−0.936865 | + | 0.349692i | \(0.886286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.0049 | 1.60793 | 0.803967 | − | 0.594674i | \(-0.202719\pi\) | ||||
0.803967 | + | 0.594674i | \(0.202719\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.28734 | −0.131916 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.44443i | 0.137998i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.2556 | − | 9.17479i | 0.930224 | − | 0.366991i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.98499i | 0.278954i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.30201 | −0.171532 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.7992 | −0.628956 | −0.314478 | − | 0.949265i | \(-0.601829\pi\) | ||||
−0.314478 | + | 0.949265i | \(0.601829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.41779i | 0.0960985i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 47.4815 | − | 4.47374i | 1.88425 | − | 0.177535i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.6088i | 1.25238i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.2892 | 0.565273 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.3861 | −1.47666 | −0.738332 | − | 0.674437i | \(-0.764386\pi\) | ||||
−0.738332 | + | 0.674437i | \(0.764386\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 44.1766i | − | 1.74216i | −0.491145 | − | 0.871078i | \(-0.663421\pi\) | ||
0.491145 | − | 0.871078i | \(-0.336579\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.10674 | − | 11.7462i | −0.0435777 | − | 0.462507i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.88521i | 0.192058i | 0.995379 | + | 0.0960288i | \(0.0306141\pi\) | ||||
−0.995379 | + | 0.0960288i | \(0.969386\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.53086 | 0.256359 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.158717 | −0.00622063 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 36.6211i | − | 1.43309i | −0.697540 | − | 0.716546i | \(-0.745722\pi\) | ||
0.697540 | − | 0.716546i | \(-0.254278\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.70189 | + | 18.0628i | 0.0664984 | + | 0.705774i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 27.0254i | − | 1.05436i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3388 | −0.402743 | −0.201371 | − | 0.979515i | \(-0.564540\pi\) | ||||
−0.201371 | + | 0.979515i | \(0.564540\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.46980 | 0.251646 | 0.125823 | − | 0.992053i | \(-0.459843\pi\) | ||||
0.125823 | + | 0.992053i | \(0.459843\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.43947i | 0.0947411i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.94109 | − | 0.182890i | 0.0752722 | − | 0.00709218i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.03291i | − | 0.272315i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.8910 | 0.421071 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 49.8426 | 1.92415 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 30.1889i | − | 1.16370i | −0.813297 | − | 0.581849i | \(-0.802330\pi\) | ||
0.813297 | − | 0.581849i | \(-0.197670\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.07009 | − | 16.1474i | −0.118168 | − | 0.621515i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.443226i | 0.0170345i | 0.999964 | + | 0.00851727i | \(0.00271117\pi\) | ||||
−0.999964 | + | 0.00851727i | \(0.997289\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.47885 | 0.171882 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.36436 | 0.243883 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.7553i | 0.985498i | 0.870171 | + | 0.492749i | \(0.164008\pi\) | ||||
−0.870171 | + | 0.492749i | \(0.835992\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.0884 | + | 1.51585i | −0.614704 | + | 0.0579178i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 15.0560i | − | 0.574422i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −49.9495 | −1.90292 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.1707 | −0.615162 | −0.307581 | − | 0.951522i | \(-0.599520\pi\) | ||||
−0.307581 | + | 0.951522i | \(0.599520\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.64802i | 0.138577i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.27439 | + | 24.1390i | 0.0862726 | + | 0.915646i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 4.30458i | − | 0.163048i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.78291 | −0.180906 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.5049 | −1.00107 | −0.500537 | − | 0.865715i | \(-0.666864\pi\) | ||||
−0.500537 | + | 0.865715i | \(0.666864\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 12.9768i | − | 0.489429i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.00423 | + | 10.6583i | 0.0378217 | + | 0.401416i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 2.57250i | − | 0.0967489i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.6885 | −1.45298 | −0.726488 | − | 0.687179i | \(-0.758849\pi\) | ||||
−0.726488 | + | 0.687179i | \(0.758849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.7000 | 0.738809 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.867829i | 0.0325004i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 44.3368 | − | 4.17744i | 1.65810 | − | 0.156227i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.31735i | 0.347963i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.7242 | 1.63064 | 0.815319 | − | 0.579012i | \(-0.196562\pi\) | ||||
0.815319 | + | 0.579012i | \(0.196562\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.0905291 | 0.00337148 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.21761i | − | 0.0452833i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.5457 | − | 6.56813i | 1.28299 | − | 0.243934i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 37.2280i | − | 1.38071i | −0.723471 | − | 0.690355i | \(-0.757455\pi\) | ||
0.723471 | − | 0.690355i | \(-0.242545\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.4686 | 0.387726 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.33921 | −0.308437 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.9656i | − | 1.03293i | −0.856308 | − | 0.516466i | \(-0.827247\pi\) | ||
0.856308 | − | 0.516466i | \(-0.172753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.91778 | − | 0.840238i | 0.328937 | − | 0.0309926i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 7.32606i | − | 0.269859i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.4555 | −1.12032 | −0.560162 | − | 0.828383i | \(-0.689261\pi\) | ||||
−0.560162 | + | 0.828383i | \(0.689261\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.35854 | −0.270323 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.97918i | 0.0726090i | 0.999341 | + | 0.0363045i | \(0.0115586\pi\) | ||||
−0.999341 | + | 0.0363045i | \(0.988441\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.65722 | − | 17.5887i | −0.0607157 | − | 0.644400i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 40.7583i | 1.49127i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.44033 | 0.162246 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.77719 | −0.210813 | −0.105406 | − | 0.994429i | \(-0.533614\pi\) | ||||
−0.105406 | + | 0.994429i | \(0.533614\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.95374i | 0.289851i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.68580 | − | 17.8920i | −0.0613525 | − | 0.651158i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 26.9857i | − | 0.980814i | −0.871494 | − | 0.490407i | \(-0.836848\pi\) | ||
0.871494 | − | 0.490407i | \(-0.163152\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.52396 | −0.0916138 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.95209 | 0.215763 | 0.107881 | − | 0.994164i | \(-0.465593\pi\) | ||||
0.107881 | + | 0.994164i | \(0.465593\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 0.555573i | − | 0.0201131i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.43913 | + | 0.512478i | −0.196652 | + | 0.0185287i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.88012i | 0.248427i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.5669 | 1.06621 | 0.533104 | − | 0.846050i | \(-0.321025\pi\) | ||||
0.533104 | + | 0.846050i | \(0.321025\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.579493 | −0.0208699 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.24223i | − | 0.0806474i | −0.999187 | − | 0.0403237i | \(-0.987161\pi\) | ||
0.999187 | − | 0.0403237i | \(-0.0128389\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.26278 | + | 0.810478i | −0.153124 | + | 0.0291132i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.857579i | 0.0307655i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.9846 | 0.465220 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.3302 | 0.834822 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 23.1195i | − | 0.826225i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.5952 | + | 0.998281i | −0.378157 | + | 0.0356302i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.28634i | 0.224084i | 0.993703 | + | 0.112042i | \(0.0357391\pi\) | ||||
−0.993703 | + | 0.112042i | \(0.964261\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.33197 | 0.189823 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.0992637 | 0.00352941 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.5081i | 1.86462i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.32778 | + | 14.0922i | 0.0470915 | + | 0.499801i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 15.5627i | − | 0.551258i | −0.961264 | − | 0.275629i | \(-0.911114\pi\) | ||
0.961264 | − | 0.275629i | \(-0.0888862\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.56687 | 0.267696 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.1137 | 1.02868 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 44.1247i | − | 1.55713i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0660856 | + | 0.701392i | 0.00232921 | + | 0.0247208i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 12.4456i | − | 0.438106i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.48638 | −0.263207 | −0.131604 | − | 0.991302i | \(-0.542013\pi\) | ||||
−0.131604 | + | 0.991302i | \(0.542013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.7694 | 1.39649 | 0.698246 | − | 0.715858i | \(-0.253964\pi\) | ||||
0.698246 | + | 0.715858i | \(0.253964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.6567i | 0.514033i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.70942 | + | 0.443724i | −0.164964 | + | 0.0155430i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 25.1548i | − | 0.880056i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.84311 | −0.134289 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.2829 | 1.05688 | 0.528440 | − | 0.848970i | \(-0.322777\pi\) | ||||
0.528440 | + | 0.848970i | \(0.322777\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.15992i | 0.249579i | 0.992183 | + | 0.124790i | \(0.0398256\pi\) | ||||
−0.992183 | + | 0.124790i | \(0.960174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.35716 | − | 12.3977i | −0.0820658 | − | 0.431632i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.1034i | 1.01202i | 0.862527 | + | 0.506011i | \(0.168881\pi\) | ||||
−0.862527 | + | 0.506011i | \(0.831119\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.4480 | 1.47428 | 0.737140 | − | 0.675740i | \(-0.236176\pi\) | ||||
0.737140 | + | 0.675740i | \(0.236176\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.8857 | 0.620449 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.33115i | − | 0.219362i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.3433 | + | 3.33007i | −1.22311 | + | 0.115242i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.85285i | 0.0986088i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.2617 | −1.11380 | −0.556898 | − | 0.830581i | \(-0.688009\pi\) | ||||
−0.556898 | + | 0.830581i | \(0.688009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.4618 | 0.705579 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.09454i | 0.0721396i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.67403 | + | 17.7671i | 0.0575884 | + | 0.611208i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.49051i | 0.0855749i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.04144 | −0.104382 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.68904 | 0.160738 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.3883i | 0.424168i | 0.977251 | + | 0.212084i | \(0.0680250\pi\) | ||||
−0.977251 | + | 0.212084i | \(0.931975\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.54587 | − | 16.4069i | −0.0528675 | − | 0.561103i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 11.8646i | − | 0.405287i | −0.979253 | − | 0.202643i | \(-0.935047\pi\) | ||
0.979253 | − | 0.202643i | \(-0.0649532\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.57949 | 0.224489 | 0.112245 | − | 0.993681i | \(-0.464196\pi\) | ||||
0.112245 | + | 0.993681i | \(0.464196\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.858092 | −0.0292437 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 41.6998i | − | 1.41948i | −0.704464 | − | 0.709739i | \(-0.748813\pi\) | ||
0.704464 | − | 0.709739i | \(-0.251187\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.170804 | + | 0.0160932i | −0.00580751 | + | 0.000547186i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.37973i | 0.318552i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.1645 | 1.09111 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.71785 | 0.261509 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 37.8571i | − | 1.28127i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.38352 | + | 0.979653i | −0.114384 | + | 0.0331183i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.9988i | 0.709079i | 0.935041 | + | 0.354540i | \(0.115362\pi\) | ||||
−0.935041 | + | 0.354540i | \(0.884638\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.10336 | −0.0372154 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.3401 | −0.415747 | −0.207874 | − | 0.978156i | \(-0.566654\pi\) | ||||
−0.207874 | + | 0.978156i | \(0.566654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 35.5426i | − | 1.19610i | −0.801457 | − | 0.598052i | \(-0.795942\pi\) | ||
0.801457 | − | 0.598052i | \(-0.204058\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.94109 | − | 0.182890i | 0.0652489 | − | 0.00614779i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.1997i | 0.644663i | 0.946627 | + | 0.322331i | \(0.104467\pi\) | ||||
−0.946627 | + | 0.322331i | \(0.895533\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.71977 | −0.225374 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.4392 | 0.885747 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.8251i | 0.763813i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.34711 | + | 46.1376i | 0.145308 | + | 1.54221i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 2.65893i | − | 0.0887792i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.10336 | −0.203558 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0048 | 0.333307 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.66237i | 0.0553202i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.42496 | + | 25.7371i | 0.0806085 | + | 0.855530i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 54.5806i | − | 1.81232i | −0.422937 | − | 0.906159i | \(-0.639001\pi\) | ||
0.422937 | − | 0.906159i | \(-0.360999\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.7439 | −0.721198 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.7619 | −0.820397 | −0.410199 | − | 0.911996i | \(-0.634541\pi\) | ||||
−0.410199 | + | 0.911996i | \(0.634541\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 66.5467i | 2.20237i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.8141 | − | 1.39579i | 0.489739 | − | 0.0461435i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.55632i | − | 0.0844172i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.32187 | 0.307500 | 0.153750 | − | 0.988110i | \(-0.450865\pi\) | ||||
0.153750 | + | 0.988110i | \(0.450865\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.63970 | −0.0540298 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.5779i | 0.808992i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.37916 | + | 23.0326i | 0.143986 | + | 0.757306i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 0.765190i | − | 0.0251321i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.9227 | 0.555217 | 0.277608 | − | 0.960694i | \(-0.410458\pi\) | ||||
0.277608 | + | 0.960694i | \(0.410458\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.0976 | 0.625900 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 9.34754i | − | 0.306025i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.88055 | + | 0.836730i | −0.290425 | + | 0.0273640i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32.3925i | − | 1.05822i | −0.848554 | − | 0.529109i | \(-0.822526\pi\) | ||
0.848554 | − | 0.529109i | \(-0.177474\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.3099 | −0.499618 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.8390 | 1.29871 | 0.649357 | − | 0.760484i | \(-0.275038\pi\) | ||||
0.649357 | + | 0.760484i | \(0.275038\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.69184i | 0.152787i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.217246 | + | 2.30571i | 0.00706700 | + | 0.0750049i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.7594i | 0.414624i | 0.978275 | + | 0.207312i | \(0.0664715\pi\) | ||||
−0.978275 | + | 0.207312i | \(0.933528\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.4844 | 1.50895 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.99880 | −0.291806 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.04791i | − | 0.228304i | −0.993463 | − | 0.114152i | \(-0.963585\pi\) | ||
0.993463 | − | 0.114152i | \(-0.0364151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.60794 | + | 48.9059i | 0.149110 | + | 1.58256i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 17.7508i | − | 0.573800i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.27688 | 0.0735244 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2469 | −0.975706 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 37.5315i | − | 1.20944i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 45.1730 | − | 4.25622i | 1.45417 | − | 0.137013i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9.27901i | − | 0.298393i | −0.988808 | − | 0.149196i | \(-0.952331\pi\) | ||
0.988808 | − | 0.149196i | \(-0.0476687\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.47390 | 0.0473484 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.0274304 | −0.000880284 | −0.000440142 | − | 1.00000i | \(-0.500140\pi\) | ||||
−0.000440142 | 1.00000i | \(0.500140\pi\) | ||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 3.41625i | − | 0.109520i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.0607 | − | 2.48322i | 0.418277 | − | 0.0795266i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 29.9665i | − | 0.958714i | −0.877620 | − | 0.479357i | \(-0.840870\pi\) | ||
0.877620 | − | 0.479357i | \(-0.159130\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.5344 | 1.51921 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.69594 | −0.149930 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.80749i | 0.185230i | 0.995702 | + | 0.0926151i | \(0.0295226\pi\) | ||||
−0.995702 | + | 0.0926151i | \(0.970477\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.1935 | + | 1.80842i | −0.611554 | + | 0.0576210i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.50841i | − | 0.0480132i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.08944 | 0.289027 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.5926 | −0.558847 | −0.279423 | − | 0.960168i | \(-0.590143\pi\) | ||||
−0.279423 | + | 0.960168i | \(0.590143\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 11.0469i | − | 0.350561i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.35861 | − | 46.2596i | −0.138177 | − | 1.46653i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.2200i | 0.767055i | 0.923530 | + | 0.383527i | \(0.125291\pi\) | ||||
−0.923530 | + | 0.383527i | \(0.874709\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.4144 | 0.487691 |
(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 | 1840.2.e.d.369.5 | 8 | ||
4.3 | odd | 2 | 115.2.b.b.24.6 | yes | 8 | ||
5.2 | odd | 4 | 9200.2.a.ck.1.3 | 4 | |||
5.3 | odd | 4 | 9200.2.a.cq.1.2 | 4 | |||
5.4 | even | 2 | inner | 1840.2.e.d.369.4 | 8 | ||
12.11 | even | 2 | 1035.2.b.e.829.3 | 8 | |||
20.3 | even | 4 | 575.2.a.i.1.3 | 4 | |||
20.7 | even | 4 | 575.2.a.j.1.2 | 4 | |||
20.19 | odd | 2 | 115.2.b.b.24.3 | ✓ | 8 | ||
60.23 | odd | 4 | 5175.2.a.bv.1.2 | 4 | |||
60.47 | odd | 4 | 5175.2.a.bw.1.3 | 4 | |||
60.59 | even | 2 | 1035.2.b.e.829.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.b.b.24.3 | ✓ | 8 | 20.19 | odd | 2 | ||
115.2.b.b.24.6 | yes | 8 | 4.3 | odd | 2 | ||
575.2.a.i.1.3 | 4 | 20.3 | even | 4 | |||
575.2.a.j.1.2 | 4 | 20.7 | even | 4 | |||
1035.2.b.e.829.3 | 8 | 12.11 | even | 2 | |||
1035.2.b.e.829.6 | 8 | 60.59 | even | 2 | |||
1840.2.e.d.369.4 | 8 | 5.4 | even | 2 | inner | ||
1840.2.e.d.369.5 | 8 | 1.1 | even | 1 | trivial | ||
5175.2.a.bv.1.2 | 4 | 60.23 | odd | 4 | |||
5175.2.a.bw.1.3 | 4 | 60.47 | odd | 4 | |||
9200.2.a.ck.1.3 | 4 | 5.2 | odd | 4 | |||
9200.2.a.cq.1.2 | 4 | 5.3 | odd | 4 |