Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(687,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.687");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.g (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: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.15582448.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 13x^{4} - 21x^{3} + 20x^{2} - 10x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 687.4 | ||
Root | \(0.500000 + 2.94141i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.687 |
Dual form | 1568.3.g.j.687.3 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.64878 | −0.549592 | −0.274796 | − | 0.961503i | \(-0.588610\pi\) | ||||
−0.274796 | + | 0.961503i | \(0.588610\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.56111i | 0.912223i | 0.889923 | + | 0.456111i | \(0.150758\pi\) | ||||
−0.889923 | + | 0.456111i | \(0.849242\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.28154 | −0.697949 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.3797 | 1.12542 | 0.562712 | − | 0.826653i | \(-0.309758\pi\) | ||||
0.562712 | + | 0.826653i | \(0.309758\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 18.3741i | − 1.41340i | −0.707516 | − | 0.706698i | \(-0.750184\pi\) | ||||
0.707516 | − | 0.706698i | \(-0.249816\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 7.52026i | − 0.501350i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.0284 | −0.766378 | −0.383189 | − | 0.923670i | \(-0.625174\pi\) | ||||
−0.383189 | + | 0.923670i | \(0.625174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.02524 | 0.159223 | 0.0796115 | − | 0.996826i | \(-0.474632\pi\) | ||||
0.0796115 | + | 0.996826i | \(0.474632\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 30.3237i | 1.31842i | 0.751958 | + | 0.659211i | \(0.229110\pi\) | ||||
−0.751958 | + | 0.659211i | \(0.770890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.19624 | 0.167850 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 25.1958 | 0.933179 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.7701i | 0.785176i | 0.919714 | + | 0.392588i | \(0.128420\pi\) | ||||
−0.919714 | + | 0.392588i | \(0.871580\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.5608i | 0.727767i | 0.931445 | + | 0.363883i | \(0.118549\pi\) | ||||
−0.931445 | + | 0.363883i | \(0.881451\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −20.4113 | −0.618524 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.7797i | 0.372423i | 0.982510 | + | 0.186212i | \(0.0596210\pi\) | ||||
−0.982510 | + | 0.186212i | \(0.940379\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 30.2948i | 0.776791i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −60.5026 | −1.47567 | −0.737837 | − | 0.674979i | \(-0.764153\pi\) | ||||
−0.737837 | + | 0.674979i | \(0.764153\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −39.0188 | −0.907414 | −0.453707 | − | 0.891151i | \(-0.649899\pi\) | ||||
−0.453707 | + | 0.891151i | \(0.649899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 28.6508i | − 0.636685i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 20.3360i | 0.432681i | 0.976318 | + | 0.216341i | \(0.0694122\pi\) | ||||
−0.976318 | + | 0.216341i | \(0.930588\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.4810 | 0.421195 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.76596i | − 0.0899237i | −0.998989 | − | 0.0449619i | \(-0.985683\pi\) | ||||
0.998989 | − | 0.0449619i | \(-0.0143166\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.4650i | 1.02664i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.98794 | −0.0875077 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.7377 | −0.198944 | −0.0994718 | − | 0.995040i | \(-0.531715\pi\) | ||||
−0.0994718 | + | 0.995040i | \(0.531715\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 108.904i | − 1.78531i | −0.450738 | − | 0.892656i | \(-0.648839\pi\) | ||||
0.450738 | − | 0.892656i | \(-0.351161\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 83.8066 | 1.28933 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 79.1994 | 1.18208 | 0.591041 | − | 0.806642i | \(-0.298717\pi\) | ||||
0.591041 | + | 0.806642i | \(0.298717\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 49.9970i | − 0.724595i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.9952i | 0.183031i | 0.995804 | + | 0.0915157i | \(0.0291712\pi\) | ||||
−0.995804 | + | 0.0915157i | \(0.970829\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −98.5819 | −1.35044 | −0.675218 | − | 0.737618i | \(-0.735951\pi\) | ||||
−0.675218 | + | 0.737618i | \(0.735951\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.91866 | −0.0922488 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 131.225i | − 1.66107i | −0.556966 | − | 0.830535i | \(-0.688035\pi\) | ||||
0.556966 | − | 0.830535i | \(-0.311965\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14.9915 | 0.185081 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −28.3732 | −0.341846 | −0.170923 | − | 0.985284i | \(-0.554675\pi\) | ||||
−0.170923 | + | 0.985284i | \(0.554675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 59.4242i | − 0.699108i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 37.5428i | − 0.431526i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −157.418 | −1.76874 | −0.884371 | − | 0.466785i | \(-0.845412\pi\) | ||||
−0.884371 | + | 0.466785i | \(0.845412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 37.1977i | − 0.399975i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.7985i | 0.145247i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −39.6175 | −0.408428 | −0.204214 | − | 0.978926i | \(-0.565464\pi\) | ||||
−0.204214 | + | 0.978926i | \(0.565464\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −77.7633 | −0.785488 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 43.6183i | − 0.431864i | −0.976408 | − | 0.215932i | \(-0.930721\pi\) | ||||
0.976408 | − | 0.215932i | \(-0.0692790\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 62.9020i | − 0.610699i | −0.952240 | − | 0.305350i | \(-0.901227\pi\) | ||||
0.952240 | − | 0.305350i | \(-0.0987734\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −44.2267 | −0.413334 | −0.206667 | − | 0.978411i | \(-0.566262\pi\) | ||||
−0.206667 | + | 0.978411i | \(0.566262\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 8.81520i | − 0.0808734i | −0.999182 | − | 0.0404367i | \(-0.987125\pi\) | ||||
0.999182 | − | 0.0404367i | \(-0.0128749\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 22.7196i | − 0.204681i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −121.408 | −1.07440 | −0.537202 | − | 0.843454i | \(-0.680519\pi\) | ||||
−0.537202 | + | 0.843454i | \(0.680519\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −138.310 | −1.20269 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 115.418i | 0.986477i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 32.2559 | 0.266578 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 99.7553 | 0.811018 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 133.167i | 1.06534i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 222.845i | − 1.75468i | −0.479868 | − | 0.877341i | \(-0.659315\pi\) | ||||
0.479868 | − | 0.877341i | \(-0.340685\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 64.3333 | 0.498708 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −237.054 | −1.80957 | −0.904785 | − | 0.425869i | \(-0.859968\pi\) | ||||
−0.904785 | + | 0.425869i | \(0.859968\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 114.921i | 0.851267i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.66276 | −0.0705311 | −0.0352656 | − | 0.999378i | \(-0.511228\pi\) | ||||
−0.0352656 | + | 0.999378i | \(0.511228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 63.0621 | 0.453684 | 0.226842 | − | 0.973932i | \(-0.427160\pi\) | ||||
0.226842 | + | 0.973932i | \(0.427160\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 33.5296i | − 0.237798i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 227.466i | − 1.59067i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −103.857 | −0.716255 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 269.912i | 1.81149i | 0.423820 | + | 0.905746i | \(0.360689\pi\) | ||||
−0.423820 | + | 0.905746i | \(0.639311\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 108.178i | 0.716408i | 0.933643 | + | 0.358204i | \(0.116611\pi\) | ||||
−0.933643 | + | 0.358204i | \(0.883389\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 81.8386 | 0.534893 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −102.902 | −0.663885 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 118.432i | 0.754343i | 0.926144 | + | 0.377171i | \(0.123103\pi\) | ||||
−0.926144 | + | 0.377171i | \(0.876897\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.85800i | 0.0494214i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 82.0284 | 0.503242 | 0.251621 | − | 0.967826i | \(-0.419036\pi\) | ||||
0.251621 | + | 0.967826i | \(0.419036\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 93.0982i | − 0.564231i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 131.596i | − 0.788002i | −0.919110 | − | 0.394001i | \(-0.871091\pi\) | ||||
0.919110 | − | 0.394001i | \(-0.128909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −168.609 | −0.997687 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.0031 | −0.111130 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 110.114i | − 0.636494i | −0.948008 | − | 0.318247i | \(-0.896906\pi\) | ||||
0.948008 | − | 0.318247i | \(-0.103094\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.3528 | 0.109338 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −153.853 | −0.859512 | −0.429756 | − | 0.902945i | \(-0.641400\pi\) | ||||
−0.429756 | + | 0.902945i | \(0.641400\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 227.511i | − 1.25697i | −0.777823 | − | 0.628484i | \(-0.783676\pi\) | ||||
0.777823 | − | 0.628484i | \(-0.216324\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 179.558i | 0.981194i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −62.8506 | −0.339733 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −161.288 | −0.862500 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 121.546i | 0.636364i | 0.948030 | + | 0.318182i | \(0.103072\pi\) | ||||
−0.948030 | + | 0.318182i | \(0.896928\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 85.4552 | 0.442773 | 0.221386 | − | 0.975186i | \(-0.428942\pi\) | ||||
0.221386 | + | 0.975186i | \(0.428942\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −138.178 | −0.708606 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 214.100i | − 1.08680i | −0.839474 | − | 0.543400i | \(-0.817137\pi\) | ||||
0.839474 | − | 0.543400i | \(-0.182863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 248.223i | 1.24735i | 0.781682 | + | 0.623677i | \(0.214362\pi\) | ||||
−0.781682 | + | 0.623677i | \(0.785638\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −130.582 | −0.649662 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 275.959i | − 1.34614i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 190.480i | − 0.920191i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 37.4514 | 0.179193 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −191.753 | −0.908783 | −0.454392 | − | 0.890802i | \(-0.650143\pi\) | ||||
−0.454392 | + | 0.890802i | \(0.650143\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 21.4262i | − 0.100593i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 177.969i | − 0.827764i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 162.539 | 0.742189 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 239.386i | 1.08320i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 41.2269i | 0.184874i | 0.995719 | + | 0.0924370i | \(0.0294657\pi\) | ||||
−0.995719 | + | 0.0924370i | \(0.970534\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26.3588 | −0.117150 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −70.4437 | −0.310325 | −0.155162 | − | 0.987889i | \(-0.549590\pi\) | ||||
−0.155162 | + | 0.987889i | \(0.549590\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 94.5190i | − 0.412747i | −0.978473 | − | 0.206373i | \(-0.933834\pi\) | ||||
0.978473 | − | 0.206373i | \(-0.0661661\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −136.287 | −0.584922 | −0.292461 | − | 0.956277i | \(-0.594474\pi\) | ||||
−0.292461 | + | 0.956277i | \(0.594474\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −92.7550 | −0.394702 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 216.360i | 0.912911i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 173.230i | 0.724813i | 0.932020 | + | 0.362406i | \(0.118045\pi\) | ||||
−0.932020 | + | 0.362406i | \(0.881955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −328.923 | −1.36483 | −0.682413 | − | 0.730967i | \(-0.739069\pi\) | ||||
−0.682413 | + | 0.730967i | \(0.739069\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −251.480 | −1.03490 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 55.5862i | − 0.225045i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 46.7811 | 0.187876 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −160.255 | −0.638466 | −0.319233 | − | 0.947676i | \(-0.603425\pi\) | ||||
−0.319233 | + | 0.947676i | \(0.603425\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 375.397i | 1.48378i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 97.9772i | 0.384224i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 145.442 | 0.565921 | 0.282960 | − | 0.959132i | \(-0.408684\pi\) | ||||
0.282960 | + | 0.959132i | \(0.408684\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 143.031i | − 0.548012i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 202.785i | − 0.771045i | −0.922698 | − | 0.385523i | \(-0.874021\pi\) | ||||
0.922698 | − | 0.385523i | \(-0.125979\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.7381 | 0.0820305 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 259.547 | 0.972087 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 221.312i | − 0.822720i | −0.911473 | − | 0.411360i | \(-0.865054\pi\) | ||||
0.911473 | − | 0.411360i | \(-0.134946\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 117.376i | − 0.433122i | −0.976269 | − | 0.216561i | \(-0.930516\pi\) | ||||
0.976269 | − | 0.216561i | \(-0.0694840\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 51.9480 | 0.188902 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 255.509i | 0.922416i | 0.887292 | + | 0.461208i | \(0.152584\pi\) | ||||
−0.887292 | + | 0.461208i | \(0.847416\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 141.716i | − 0.507944i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −278.004 | −0.989336 | −0.494668 | − | 0.869082i | \(-0.664710\pi\) | ||||
−0.494668 | + | 0.869082i | \(0.664710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −56.6896 | −0.200317 | −0.100158 | − | 0.994972i | \(-0.531935\pi\) | ||||
−0.100158 | + | 0.994972i | \(0.531935\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 22.7506i | − 0.0798266i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −119.260 | −0.412664 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 65.3204 | 0.224469 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 287.871i | 0.982493i | 0.871020 | + | 0.491247i | \(0.163459\pi\) | ||||
−0.871020 | + | 0.491247i | \(0.836541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 53.5369i | − 0.181481i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 311.916 | 1.05022 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 557.172 | 1.86345 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 71.9168i | 0.237349i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 496.724 | 1.62860 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −53.6483 | −0.174750 | −0.0873750 | − | 0.996175i | \(-0.527848\pi\) | ||||
−0.0873750 | + | 0.996175i | \(0.527848\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 103.711i | 0.335636i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 105.108i | 0.337968i | 0.985619 | + | 0.168984i | \(0.0540487\pi\) | ||||
−0.985619 | + | 0.168984i | \(0.945951\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 210.490 | 0.672492 | 0.336246 | − | 0.941774i | \(-0.390843\pi\) | ||||
0.336246 | + | 0.941774i | \(0.390843\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 62.8880i | 0.198385i | 0.995068 | + | 0.0991925i | \(0.0316259\pi\) | ||||
−0.995068 | + | 0.0991925i | \(0.968374\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 281.886i | 0.883655i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 72.9199 | 0.227165 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −39.4141 | −0.122025 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 77.1023i | − 0.237238i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.5343i | 0.0444474i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −196.579 | −0.593893 | −0.296947 | − | 0.954894i | \(-0.595968\pi\) | ||||
−0.296947 | + | 0.954894i | \(0.595968\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 86.5575i | − 0.259932i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 361.238i | 1.07832i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 591.516 | 1.75524 | 0.877620 | − | 0.479358i | \(-0.159130\pi\) | ||||
0.877620 | + | 0.479358i | \(0.159130\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 200.174 | 0.590484 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 279.295i | 0.819046i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 228.042 | 0.660992 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −247.540 | −0.713371 | −0.356685 | − | 0.934225i | \(-0.616093\pi\) | ||||
−0.356685 | + | 0.934225i | \(0.616093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 288.749i | − 0.827362i | −0.910422 | − | 0.413681i | \(-0.864243\pi\) | ||||
0.910422 | − | 0.413681i | \(-0.135757\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 462.952i | − 1.31895i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.26966 | −0.00359677 | −0.00179839 | − | 0.999998i | \(-0.500572\pi\) | ||||
−0.00179839 | + | 0.999998i | \(0.500572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −59.2727 | −0.166965 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.4021i | 0.0484738i | 0.999706 | + | 0.0242369i | \(0.00771560\pi\) | ||||
−0.999706 | + | 0.0242369i | \(0.992284\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −351.848 | −0.974648 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −53.1828 | −0.146509 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 449.643i | − 1.23190i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 530.032i | − 1.44423i | −0.691773 | − | 0.722115i | \(-0.743170\pi\) | ||||
0.691773 | − | 0.722115i | \(-0.256830\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 380.049 | 1.02994 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 118.613i | − 0.317998i | −0.987279 | − | 0.158999i | \(-0.949173\pi\) | ||||
0.987279 | − | 0.158999i | \(-0.0508267\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 219.563i | − 0.585502i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 418.381 | 1.10976 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 345.947 | 0.912790 | 0.456395 | − | 0.889777i | \(-0.349140\pi\) | ||||
0.456395 | + | 0.889777i | \(0.349140\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 367.421i | 0.964359i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 404.873i | 1.05711i | 0.848899 | + | 0.528555i | \(0.177266\pi\) | ||||
−0.848899 | + | 0.528555i | \(0.822734\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 245.098 | 0.633328 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 134.397i | − 0.345493i | −0.984966 | − | 0.172747i | \(-0.944736\pi\) | ||||
0.984966 | − | 0.172747i | \(-0.0552642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 395.070i | − 1.01041i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 390.848 | 0.994525 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 598.530 | 1.51527 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 612.481i | 1.54277i | 0.636367 | + | 0.771386i | \(0.280436\pi\) | ||||
−0.636367 | + | 0.771386i | \(0.719564\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −126.247 | −0.314830 | −0.157415 | − | 0.987533i | \(-0.550316\pi\) | ||||
−0.157415 | + | 0.987533i | \(0.550316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 414.535 | 1.02862 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 68.3781i | 0.168835i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 170.588i | 0.419134i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 342.519 | 0.837455 | 0.418727 | − | 0.908112i | \(-0.362476\pi\) | ||||
0.418727 | + | 0.908112i | \(0.362476\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.9317 | 0.0387634 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 129.414i | − 0.311840i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −103.975 | −0.249341 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 376.392 | 0.898311 | 0.449155 | − | 0.893454i | \(-0.351725\pi\) | ||||
0.449155 | + | 0.893454i | \(0.351725\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 111.135i | − 0.263978i | −0.991251 | − | 0.131989i | \(-0.957864\pi\) | ||||
0.991251 | − | 0.131989i | \(-0.0421363\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 127.742i | − 0.301989i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −54.6704 | −0.128636 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 375.040i | 0.874219i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 41.2784i | − 0.0957734i | −0.998853 | − | 0.0478867i | \(-0.984751\pi\) | ||||
0.998853 | − | 0.0478867i | \(-0.0152486\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −675.176 | −1.55930 | −0.779649 | − | 0.626217i | \(-0.784603\pi\) | ||||
−0.779649 | + | 0.626217i | \(0.784603\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 171.237 | 0.393648 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 91.7365i | 0.209923i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 530.256i | 1.20787i | 0.797032 | + | 0.603936i | \(0.206402\pi\) | ||||
−0.797032 | + | 0.603936i | \(0.793598\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −332.033 | −0.749510 | −0.374755 | − | 0.927124i | \(-0.622273\pi\) | ||||
−0.374755 | + | 0.927124i | \(0.622273\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 718.002i | − 1.61349i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 445.025i | − 0.995582i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.4200 | −0.0432517 | −0.0216259 | − | 0.999766i | \(-0.506884\pi\) | ||||
−0.0216259 | + | 0.999766i | \(0.506884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −749.002 | −1.66076 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 178.361i | − 0.393732i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −177.959 | −0.389408 | −0.194704 | − | 0.980862i | \(-0.562375\pi\) | ||||
−0.194704 | + | 0.980862i | \(0.562375\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −328.262 | −0.715168 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 299.341i | − 0.649329i | −0.945829 | − | 0.324664i | \(-0.894749\pi\) | ||||
0.945829 | − | 0.324664i | \(-0.105251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 505.213i | 1.09117i | 0.838055 | + | 0.545586i | \(0.183693\pi\) | ||||
−0.838055 | + | 0.545586i | \(0.816307\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 169.663 | 0.364866 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 650.324 | 1.39256 | 0.696278 | − | 0.717772i | \(-0.254838\pi\) | ||||
0.696278 | + | 0.717772i | \(0.254838\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 195.268i | − 0.414581i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −483.039 | −1.02122 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.6946 | 0.0267255 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.9375i | 0.0627621i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 660.951i | 1.37986i | 0.723878 | + | 0.689928i | \(0.242358\pi\) | ||||
−0.723878 | + | 0.689928i | \(0.757642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 253.190 | 0.526382 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 180.700i | − 0.372577i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 386.100i | 0.792813i | 0.918075 | + | 0.396407i | \(0.129743\pi\) | ||||
−0.918075 | + | 0.396407i | \(0.870257\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −135.246 | −0.276578 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 898.359 | 1.82965 | 0.914826 | − | 0.403848i | \(-0.132328\pi\) | ||||
0.914826 | + | 0.403848i | \(0.132328\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 296.659i | − 0.601742i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 354.687i | − 0.716540i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −791.176 | −1.58552 | −0.792761 | − | 0.609532i | \(-0.791357\pi\) | ||||
−0.792761 | + | 0.609532i | \(0.791357\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 216.973i | 0.433080i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 798.990i | 1.58845i | 0.607624 | + | 0.794225i | \(0.292123\pi\) | ||||
−0.607624 | + | 0.794225i | \(0.707877\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 198.948 | 0.393956 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 277.999 | 0.548321 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 551.106i | − 1.08272i | −0.840790 | − | 0.541362i | \(-0.817909\pi\) | ||||
0.840790 | − | 0.541362i | \(-0.182091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 76.2234 | 0.148584 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 286.903 | 0.557094 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 251.753i | 0.486950i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 181.553i | 0.349812i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 142.783 | 0.274055 | 0.137028 | − | 0.990567i | \(-0.456245\pi\) | ||||
0.137028 | + | 0.990567i | \(0.456245\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 832.511 | 1.59180 | 0.795900 | − | 0.605429i | \(-0.206998\pi\) | ||||
0.795900 | + | 0.605429i | \(0.206998\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 293.931i | − 0.557745i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −390.528 | −0.738238 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 73.7306 | 0.138852 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1111.68i | 2.08571i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 201.723i | − 0.377052i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 253.669 | 0.472381 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 616.465i | 1.13949i | 0.821821 | + | 0.569746i | \(0.192958\pi\) | ||||
−0.821821 | + | 0.569746i | \(0.807042\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 375.115i | 0.690819i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.2071 | 0.0737746 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −577.704 | −1.05613 | −0.528065 | − | 0.849204i | \(-0.677082\pi\) | ||||
−0.528065 | + | 0.849204i | \(0.677082\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 684.085i | 1.24606i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 68.8850i | 0.125018i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 103.627 | 0.186715 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 514.710i | 0.924075i | 0.886860 | + | 0.462038i | \(0.152881\pi\) | ||||
−0.886860 | + | 0.462038i | \(0.847119\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 716.937i | 1.28253i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 265.927 | 0.474023 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 608.719 | 1.08121 | 0.540603 | − | 0.841278i | \(-0.318196\pi\) | ||||
0.540603 | + | 0.841278i | \(0.318196\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 553.754i | − 0.980096i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 186.374 | 0.327547 | 0.163774 | − | 0.986498i | \(-0.447633\pi\) | ||||
0.163774 | + | 0.986498i | \(0.447633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −183.776 | −0.321849 | −0.160924 | − | 0.986967i | \(-0.551448\pi\) | ||||
−0.160924 | + | 0.986967i | \(0.551448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 200.401i | − 0.349741i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 127.246i | 0.221297i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 134.456 | 0.233026 | 0.116513 | − | 0.993189i | \(-0.462828\pi\) | ||||
0.116513 | + | 0.993189i | \(0.462828\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −140.896 | −0.243345 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 59.0009i | − 0.101202i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −526.434 | −0.899887 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 921.405 | 1.56968 | 0.784842 | − | 0.619696i | \(-0.212744\pi\) | ||||
0.784842 | + | 0.619696i | \(0.212744\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 68.2517i | 0.115877i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 353.002i | 0.597297i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 96.3746 | 0.162520 | 0.0812602 | − | 0.996693i | \(-0.474106\pi\) | ||||
0.0812602 | + | 0.996693i | \(0.474106\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 409.265i | − 0.685536i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 167.098i | − 0.278961i | −0.990225 | − | 0.139481i | \(-0.955457\pi\) | ||||
0.990225 | − | 0.139481i | \(-0.0445433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 88.4635 | 0.147194 | 0.0735969 | − | 0.997288i | \(-0.476552\pi\) | ||||
0.0735969 | + | 0.997288i | \(0.476552\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −497.494 | −0.825032 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 147.123i | 0.243178i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 55.5692i | − 0.0915472i | −0.998952 | − | 0.0457736i | \(-0.985425\pi\) | ||||
0.998952 | − | 0.0457736i | \(-0.0145753\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 373.657 | 0.611550 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 869.117i | − 1.41781i | −0.705304 | − | 0.708905i | \(-0.749190\pi\) | ||||
0.705304 | − | 0.708905i | \(-0.250810\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 454.995i | 0.739829i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −249.359 | −0.404147 | −0.202074 | − | 0.979370i | \(-0.564768\pi\) | ||||
−0.202074 | + | 0.979370i | \(0.564768\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 497.673 | 0.803995 | 0.401998 | − | 0.915641i | \(-0.368316\pi\) | ||||
0.401998 | + | 0.915641i | \(0.368316\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 764.031i | 1.23032i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −502.486 | −0.803977 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −61.7490 | −0.0984833 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 179.527i | − 0.285417i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 172.763i | − 0.273792i | −0.990585 | − | 0.136896i | \(-0.956287\pi\) | ||||
0.990585 | − | 0.136896i | \(-0.0437126\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 316.158 | 0.499460 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1016.42 | 1.60066 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 81.6300i | − 0.127746i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −427.898 | −0.667547 | −0.333774 | − | 0.942653i | \(-0.608322\pi\) | ||||
−0.333774 | + | 0.942653i | \(0.608322\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.9463 | 0.0247998 | 0.0123999 | − | 0.999923i | \(-0.496053\pi\) | ||||
0.0123999 | + | 0.999923i | \(0.496053\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 293.431i | 0.454932i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 520.204i | 0.804025i | 0.915634 | + | 0.402012i | \(0.131689\pi\) | ||||
−0.915634 | + | 0.402012i | \(0.868311\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −145.308 | −0.223896 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 424.568i | − 0.650181i | −0.945683 | − | 0.325091i | \(-0.894605\pi\) | ||||
0.945683 | − | 0.325091i | \(-0.105395\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1081.23i | − 1.65073i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 619.246 | 0.942535 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −304.044 | −0.461372 | −0.230686 | − | 0.973028i | \(-0.574097\pi\) | ||||
−0.230686 | + | 0.973028i | \(0.574097\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 179.108i | − 0.270966i | −0.990780 | − | 0.135483i | \(-0.956741\pi\) | ||||
0.990780 | − | 0.135483i | \(-0.0432586\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 394.694i | − 0.595316i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −690.474 | −1.03519 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 67.9739i | − 0.101605i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1348.20i | − 2.00923i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 544.352 | 0.808844 | 0.404422 | − | 0.914573i | \(-0.367473\pi\) | ||||
0.404422 | + | 0.914573i | \(0.367473\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 105.728 | 0.156634 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 544.344i | − 0.804053i | −0.915628 | − | 0.402027i | \(-0.868306\pi\) | ||||
0.915628 | − | 0.402027i | \(-0.131694\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 116.146 | 0.170552 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −886.988 | −1.29866 | −0.649332 | − | 0.760505i | \(-0.724951\pi\) | ||||
−0.649332 | + | 0.760505i | \(0.724951\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 44.0730i | − 0.0643401i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 155.841i | 0.226842i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −87.5704 | −0.127098 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1178.48 | −1.70548 | −0.852738 | − | 0.522340i | \(-0.825059\pi\) | ||||
−0.852738 | + | 0.522340i | \(0.825059\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 287.633i | 0.413861i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 788.254 | 1.13092 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 224.706 | 0.321468 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 901.601i | − 1.28616i | −0.765797 | − | 0.643082i | \(-0.777655\pi\) | ||||
0.765797 | − | 0.643082i | \(-0.222345\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.6868i | 0.0592984i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 152.932 | 0.216925 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 332.802i | − 0.469397i | −0.972068 | − | 0.234698i | \(-0.924590\pi\) | ||||
0.972068 | − | 0.234698i | \(-0.0754102\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 824.292i | 1.15934i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −684.126 | −0.959504 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1037.50 | 1.45104 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 285.618i | − 0.398351i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1184.95i | 1.64805i | 0.566551 | + | 0.824027i | \(0.308277\pi\) | ||||
−0.566551 | + | 0.824027i | \(0.691723\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 542.320 | 0.750097 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 95.5488i | 0.131791i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.9398i | 0.0274275i | 0.999906 | + | 0.0137138i | \(0.00436536\pi\) | ||||
−0.999906 | + | 0.0137138i | \(0.995635\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 279.711 | 0.383691 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 508.354 | 0.695423 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1037.30i | 1.41514i | 0.706644 | + | 0.707569i | \(0.250208\pi\) | ||||
−0.706644 | + | 0.707569i | \(0.749792\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 980.462 | 1.33034 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 419.971 | 0.568297 | 0.284148 | − | 0.958780i | \(-0.408289\pi\) | ||||
0.284148 | + | 0.958780i | \(0.408289\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 91.6491i | 0.123683i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1241.67i | − 1.67116i | −0.549370 | − | 0.835579i | \(-0.685132\pi\) | ||||
0.549370 | − | 0.835579i | \(-0.314868\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1231.10 | −1.65249 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 178.227 | 0.238591 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 647.797i | 0.862579i | 0.902214 | + | 0.431289i | \(0.141941\pi\) | ||||
−0.902214 | + | 0.431289i | \(0.858059\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 264.225 | 0.350896 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −493.411 | −0.653524 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 105.310i | 0.139116i | 0.997578 | + | 0.0695578i | \(0.0221588\pi\) | ||||
−0.997578 | + | 0.0695578i | \(0.977841\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 618.946i | − 0.815476i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −421.884 | −0.554381 | −0.277190 | − | 0.960815i | \(-0.589403\pi\) | ||||
−0.277190 | + | 0.960815i | \(0.589403\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 373.275i | 0.487941i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 215.670i | 0.281186i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −189.767 | −0.246772 | −0.123386 | − | 0.992359i | \(-0.539375\pi\) | ||||
−0.123386 | + | 0.992359i | \(0.539375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −239.801 | −0.311025 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 842.788i | − 1.09028i | −0.838345 | − | 0.545141i | \(-0.816476\pi\) | ||||
0.838345 | − | 0.545141i | \(-0.183524\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 94.6704i | 0.122155i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −183.035 | −0.234961 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 160.876i | 0.205988i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 573.712i | 0.732710i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −540.181 | −0.688128 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1494.20 | −1.89860 | −0.949298 | − | 0.314376i | \(-0.898205\pi\) | ||||
−0.949298 | + | 0.314376i | \(0.898205\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 334.347i | 0.423760i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2001.02 | −2.52335 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −35.8412 | −0.0450833 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 292.040i | − 0.366424i | −0.983073 | − | 0.183212i | \(-0.941351\pi\) | ||||
0.983073 | − | 0.183212i | \(-0.0586494\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 264.947i | − 0.331598i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 988.827 | 1.23449 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1220.41 | −1.51981 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 364.893i | 0.452160i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 156.906 | 0.193951 | 0.0969754 | − | 0.995287i | \(-0.469083\pi\) | ||||
0.0969754 | + | 0.995287i | \(0.469083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1183.00 | −1.45869 | −0.729347 | − | 0.684144i | \(-0.760176\pi\) | ||||
−0.729347 | + | 0.684144i | \(0.760176\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 193.527i | 0.238040i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 374.141i | 0.459068i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −118.041 | −0.144481 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 185.415i | 0.225840i | 0.993604 | + | 0.112920i | \(0.0360204\pi\) | ||||
−0.993604 | + | 0.112920i | \(0.963980\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 652.316i | − 0.792608i | −0.918119 | − | 0.396304i | \(-0.870293\pi\) | ||||
0.918119 | − | 0.396304i | \(-0.129707\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −85.6506 | −0.103819 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 829.430 | 1.00294 | 0.501469 | − | 0.865176i | \(-0.332793\pi\) | ||||
0.501469 | + | 0.865176i | \(0.332793\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 755.129i | − 0.910892i | −0.890263 | − | 0.455446i | \(-0.849480\pi\) | ||||
0.890263 | − | 0.455446i | \(-0.150520\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 421.277i | − 0.506952i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 600.226 | 0.718834 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 568.437i | 0.679137i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 88.6147i | − 0.105619i | −0.998605 | − | 0.0528097i | \(-0.983182\pi\) | ||||
0.998605 | − | 0.0528097i | \(-0.0168177\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 322.522 | 0.383499 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 458.366 | 0.543731 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 769.045i | − 0.910113i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 93.4685 | 0.110092 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −417.851 | −0.491011 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 367.466i | 0.430792i | 0.976527 | + | 0.215396i | \(0.0691042\pi\) | ||||
−0.976527 | + | 0.215396i | \(0.930896\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 86.6755i | − 0.101375i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −165.340 | −0.192928 | −0.0964642 | − | 0.995336i | \(-0.530753\pi\) | ||||
−0.0964642 | + | 0.995336i | \(0.530753\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 650.972 | 0.757825 | 0.378913 | − | 0.925432i | \(-0.376298\pi\) | ||||
0.378913 | + | 0.925432i | \(0.376298\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 136.736i | − 0.158442i | −0.996857 | − | 0.0792212i | \(-0.974757\pi\) | ||||
0.996857 | − | 0.0792212i | \(-0.0252433\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 502.240 | 0.580625 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 196.633 | 0.226797 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1624.51i | − 1.86941i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1455.22i | − 1.67075i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 248.859 | 0.285062 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 176.502i | 0.201256i | 0.994924 | + | 0.100628i | \(0.0320852\pi\) | ||||
−0.994924 | + | 0.100628i | \(0.967915\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 474.634i | − 0.539971i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 734.879 | 0.834142 | 0.417071 | − | 0.908874i | \(-0.363057\pi\) | ||||
0.417071 | + | 0.908874i | \(0.363057\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −872.637 | −0.988264 | −0.494132 | − | 0.869387i | \(-0.664514\pi\) | ||||
−0.494132 | + | 0.869387i | \(0.664514\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 88.2703i | 0.0997405i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 24.0981i | − 0.0271681i | −0.999908 | − | 0.0135840i | \(-0.995676\pi\) | ||||
0.999908 | − | 0.0135840i | \(-0.00432407\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 185.590 | 0.208294 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 61.5213i | 0.0688929i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 701.740i | − 0.784067i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −918.652 | −1.02414 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −513.711 | −0.571425 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62.0930i | 0.0689156i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1037.70 | 1.14663 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1413.31 | 1.55822 | 0.779110 | − | 0.626887i | \(-0.215671\pi\) | ||||
0.779110 | + | 0.626887i | \(0.215671\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 273.990i | 0.301419i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1778.28i | 1.95201i | 0.217746 | + | 0.976005i | \(0.430129\pi\) | ||||
−0.217746 | + | 0.976005i | \(0.569871\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −351.251 | −0.384722 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −818.987 | −0.895067 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 893.841i | − 0.972624i | −0.873785 | − | 0.486312i | \(-0.838342\pi\) | ||||
0.873785 | − | 0.486312i | \(-0.161658\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 88.4540 | 0.0960413 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 238.776 | 0.258696 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 57.8228i | 0.0625111i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 395.122i | 0.426237i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −729.460 | −0.785210 | −0.392605 | − | 0.919707i | \(-0.628426\pi\) | ||||
−0.392605 | + | 0.919707i | \(0.628426\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 173.300i | − 0.185745i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 735.651i | − 0.786792i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 637.240 | 0.680085 | 0.340042 | − | 0.940410i | \(-0.389559\pi\) | ||||
0.340042 | + | 0.940410i | \(0.389559\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −347.051 | −0.369596 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1753.57i | 1.86352i | 0.363072 | + | 0.931761i | \(0.381728\pi\) | ||||
−0.363072 | + | 0.931761i | \(0.618272\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1834.66i | − 1.94556i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 873.993 | 0.922907 | 0.461453 | − | 0.887164i | \(-0.347328\pi\) | ||||
0.461453 | + | 0.887164i | \(0.347328\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1811.36i | 1.90870i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 103.688i | − 0.109031i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −880.208 | −0.923618 | −0.461809 | − | 0.886979i | \(-0.652800\pi\) | ||||
−0.461809 | + | 0.886979i | \(0.652800\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −554.383 | −0.580506 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 464.767i | − 0.485650i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 452.012 | 0.470356 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 277.812 | 0.288486 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 389.771i | 0.403908i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 259.016i | 0.267855i | 0.990991 | + | 0.133928i | \(0.0427590\pi\) | ||||
−0.990991 | + | 0.133928i | \(0.957241\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 64.9851 | 0.0670640 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 432.650 | 0.445572 | 0.222786 | − | 0.974867i | \(-0.428485\pi\) | ||||
0.222786 | + | 0.974867i | \(0.428485\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 127.124i | 0.130384i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 815.509 | 0.834708 | 0.417354 | − | 0.908744i | \(-0.362958\pi\) | ||||
0.417354 | + | 0.908744i | \(0.362958\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1948.78 | −1.99058 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 55.3730i | 0.0564455i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 139.412i | 0.141823i | 0.997483 | + | 0.0709116i | \(0.0225908\pi\) | ||||
−0.997483 | + | 0.0709116i | \(0.977409\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 976.533 | 0.991404 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1183.20i | − 1.19636i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1548.78i | 1.56285i | 0.624002 | + | 0.781423i | \(0.285506\pi\) | ||||
−0.624002 | + | 0.781423i | \(0.714494\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 324.114 | 0.326399 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1132.18 | −1.13786 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1282.50i | 1.28636i | 0.765717 | + | 0.643178i | \(0.222384\pi\) | ||||
−0.765717 | + | 0.643178i | \(0.777616\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 347.190i | 0.347538i |
(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 | 1568.3.g.j.687.4 | 6 | ||
4.3 | odd | 2 | 392.3.g.j.99.2 | 6 | |||
7.2 | even | 3 | 224.3.o.d.207.4 | 12 | |||
7.4 | even | 3 | 224.3.o.d.79.3 | 12 | |||
7.6 | odd | 2 | 1568.3.g.l.687.3 | 6 | |||
8.3 | odd | 2 | inner | 1568.3.g.j.687.3 | 6 | ||
8.5 | even | 2 | 392.3.g.j.99.1 | 6 | |||
28.3 | even | 6 | 392.3.k.l.275.4 | 12 | |||
28.11 | odd | 6 | 56.3.k.d.51.4 | yes | 12 | ||
28.19 | even | 6 | 392.3.k.l.67.5 | 12 | |||
28.23 | odd | 6 | 56.3.k.d.11.5 | yes | 12 | ||
28.27 | even | 2 | 392.3.g.i.99.2 | 6 | |||
56.5 | odd | 6 | 392.3.k.l.67.4 | 12 | |||
56.11 | odd | 6 | 224.3.o.d.79.4 | 12 | |||
56.13 | odd | 2 | 392.3.g.i.99.1 | 6 | |||
56.27 | even | 2 | 1568.3.g.l.687.4 | 6 | |||
56.37 | even | 6 | 56.3.k.d.11.4 | ✓ | 12 | ||
56.45 | odd | 6 | 392.3.k.l.275.5 | 12 | |||
56.51 | odd | 6 | 224.3.o.d.207.3 | 12 | |||
56.53 | even | 6 | 56.3.k.d.51.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.k.d.11.4 | ✓ | 12 | 56.37 | even | 6 | ||
56.3.k.d.11.5 | yes | 12 | 28.23 | odd | 6 | ||
56.3.k.d.51.4 | yes | 12 | 28.11 | odd | 6 | ||
56.3.k.d.51.5 | yes | 12 | 56.53 | even | 6 | ||
224.3.o.d.79.3 | 12 | 7.4 | even | 3 | |||
224.3.o.d.79.4 | 12 | 56.11 | odd | 6 | |||
224.3.o.d.207.3 | 12 | 56.51 | odd | 6 | |||
224.3.o.d.207.4 | 12 | 7.2 | even | 3 | |||
392.3.g.i.99.1 | 6 | 56.13 | odd | 2 | |||
392.3.g.i.99.2 | 6 | 28.27 | even | 2 | |||
392.3.g.j.99.1 | 6 | 8.5 | even | 2 | |||
392.3.g.j.99.2 | 6 | 4.3 | odd | 2 | |||
392.3.k.l.67.4 | 12 | 56.5 | odd | 6 | |||
392.3.k.l.67.5 | 12 | 28.19 | even | 6 | |||
392.3.k.l.275.4 | 12 | 28.3 | even | 6 | |||
392.3.k.l.275.5 | 12 | 56.45 | odd | 6 | |||
1568.3.g.j.687.3 | 6 | 8.3 | odd | 2 | inner | ||
1568.3.g.j.687.4 | 6 | 1.1 | even | 1 | trivial | ||
1568.3.g.l.687.3 | 6 | 7.6 | odd | 2 | |||
1568.3.g.l.687.4 | 6 | 56.27 | even | 2 |