Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(721,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.o (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: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 80 x^{18} - 152 x^{17} + 4326 x^{16} - 10096 x^{15} + 70116 x^{14} - 93436 x^{13} + \cdots + 36100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{37} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.10 | ||
Root | \(-1.34238 - 2.32507i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.721 |
Dual form | 2736.3.o.r.721.9 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0118390 | 0.00236781 | 0.00118390 | − | 0.999999i | \(-0.499623\pi\) | ||||
0.00118390 | + | 0.999999i | \(0.499623\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.38136 | −0.768765 | −0.384383 | − | 0.923174i | \(-0.625586\pi\) | ||||
−0.384383 | + | 0.923174i | \(0.625586\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.1709 | −1.83372 | −0.916859 | − | 0.399211i | \(-0.869284\pi\) | ||||
−0.916859 | + | 0.399211i | \(0.869284\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.7435i | 1.44181i | 0.693035 | + | 0.720904i | \(0.256273\pi\) | ||||
−0.693035 | + | 0.720904i | \(0.743727\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.61324 | 0.153720 | 0.0768600 | − | 0.997042i | \(-0.475511\pi\) | ||||
0.0768600 | + | 0.997042i | \(0.475511\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.1212 | − | 12.7119i | −0.743219 | − | 0.669049i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.3236 | 0.535810 | 0.267905 | − | 0.963445i | \(-0.413669\pi\) | ||||
0.267905 | + | 0.963445i | \(0.413669\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.9999 | −0.999994 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.07280i | − | 0.140441i | −0.997531 | − | 0.0702206i | \(-0.977630\pi\) | ||
0.997531 | − | 0.0702206i | \(-0.0223703\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.9617i | 0.482635i | 0.970446 | + | 0.241317i | \(0.0775795\pi\) | ||||
−0.970446 | + | 0.241317i | \(0.922421\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0637101 | −0.00182029 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 62.7522i | 1.69601i | 0.529992 | + | 0.848003i | \(0.322195\pi\) | ||||
−0.529992 | + | 0.848003i | \(0.677805\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 46.8535i | − | 1.14277i | −0.820683 | − | 0.571384i | \(-0.806407\pi\) | ||
0.820683 | − | 0.571384i | \(-0.193593\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 72.6553 | 1.68966 | 0.844829 | − | 0.535037i | \(-0.179702\pi\) | ||||
0.844829 | + | 0.535037i | \(0.179702\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −81.3241 | −1.73030 | −0.865150 | − | 0.501512i | \(-0.832777\pi\) | ||||
−0.865150 | + | 0.501512i | \(0.832777\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −20.0410 | −0.409000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 32.5146i | − | 0.613483i | −0.951793 | − | 0.306741i | \(-0.900761\pi\) | ||
0.951793 | − | 0.306741i | \(-0.0992387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.238804 | −0.00434189 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 48.9963i | − | 0.830446i | −0.909720 | − | 0.415223i | \(-0.863704\pi\) | ||
0.909720 | − | 0.415223i | \(-0.136296\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 81.6937 | 1.33924 | 0.669620 | − | 0.742704i | \(-0.266457\pi\) | ||||
0.669620 | + | 0.742704i | \(0.266457\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.221905i | 0.00341392i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 64.8329i | − | 0.967655i | −0.875164 | − | 0.483827i | \(-0.839246\pi\) | ||
0.875164 | − | 0.483827i | \(-0.160754\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 18.7083i | − | 0.263498i | −0.991283 | − | 0.131749i | \(-0.957941\pi\) | ||
0.991283 | − | 0.131749i | \(-0.0420592\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 117.506 | 1.60966 | 0.804832 | − | 0.593502i | \(-0.202255\pi\) | ||||
0.804832 | + | 0.593502i | \(0.202255\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 108.547 | 1.40970 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 80.1054i | 1.01399i | 0.861948 | + | 0.506996i | \(0.169244\pi\) | ||||
−0.861948 | + | 0.506996i | \(0.830756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 61.0368 | 0.735383 | 0.367692 | − | 0.929948i | \(-0.380148\pi\) | ||||
0.367692 | + | 0.929948i | \(0.380148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0309383 | 0.000363979 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 132.639i | 1.49032i | 0.666884 | + | 0.745162i | \(0.267628\pi\) | ||||
−0.666884 | + | 0.745162i | \(0.732372\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 100.865i | − | 1.10841i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.167181 | − | 0.150497i | −0.00175980 | − | 0.00158418i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 91.8294i | 0.946695i | 0.880876 | + | 0.473347i | \(0.156954\pi\) | ||||
−0.880876 | + | 0.473347i | \(0.843046\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.18062 | 0.0413923 | 0.0206961 | − | 0.999786i | \(-0.493412\pi\) | ||||
0.0206961 | + | 0.999786i | \(0.493412\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 49.0424i | − | 0.476140i | −0.971248 | − | 0.238070i | \(-0.923485\pi\) | ||
0.971248 | − | 0.238070i | \(-0.0765148\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 123.082i | − | 1.15030i | −0.818049 | − | 0.575149i | \(-0.804944\pi\) | ||
0.818049 | − | 0.575149i | \(-0.195056\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 40.7625i | − | 0.373968i | −0.982363 | − | 0.186984i | \(-0.940129\pi\) | ||
0.982363 | − | 0.186984i | \(-0.0598712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 188.610i | − | 1.66911i | −0.550921 | − | 0.834557i | \(-0.685723\pi\) | ||
0.550921 | − | 0.834557i | \(-0.314277\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.145900 | 0.00126870 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.0628 | −0.118175 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 285.865 | 2.36252 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.591950 | −0.00473560 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 189.176i | − | 1.48958i | −0.667300 | − | 0.744789i | \(-0.732550\pi\) | ||
0.667300 | − | 0.744789i | \(-0.267450\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 57.7649 | 0.440953 | 0.220477 | − | 0.975392i | \(-0.429239\pi\) | ||||
0.220477 | + | 0.975392i | \(0.429239\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 75.9910 | + | 68.4074i | 0.571361 | + | 0.514341i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −190.267 | −1.38881 | −0.694406 | − | 0.719584i | \(-0.744333\pi\) | ||||
−0.694406 | + | 0.719584i | \(0.744333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −59.9097 | −0.431005 | −0.215502 | − | 0.976503i | \(-0.569139\pi\) | ||||
−0.215502 | + | 0.976503i | \(0.569139\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 378.073i | − | 2.64387i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.0482180i | − | 0.000332538i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 126.063 | 0.846063 | 0.423032 | − | 0.906115i | \(-0.360966\pi\) | ||||
0.423032 | + | 0.906115i | \(0.360966\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 255.446i | 1.69170i | 0.533422 | + | 0.845849i | \(0.320906\pi\) | ||||
−0.533422 | + | 0.845849i | \(0.679094\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.177132i | 0.00114279i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 52.9750 | 0.337421 | 0.168710 | − | 0.985666i | \(-0.446040\pi\) | ||||
0.168710 | + | 0.985666i | \(0.446040\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −66.3179 | −0.411912 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −260.416 | −1.59765 | −0.798823 | − | 0.601566i | \(-0.794544\pi\) | ||||
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 283.157i | − | 1.69555i | −0.530357 | − | 0.847774i | \(-0.677942\pi\) | ||
0.530357 | − | 0.847774i | \(-0.322058\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −182.319 | −1.07881 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 97.1696i | − | 0.561674i | −0.959755 | − | 0.280837i | \(-0.909388\pi\) | ||
0.959755 | − | 0.280837i | \(-0.0906120\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 134.533 | 0.768761 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 309.155i | 1.72712i | 0.504245 | + | 0.863560i | \(0.331771\pi\) | ||||
−0.504245 | + | 0.863560i | \(0.668229\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 62.7290i | − | 0.346569i | −0.984872 | − | 0.173284i | \(-0.944562\pi\) | ||
0.984872 | − | 0.173284i | \(-0.0554380\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.742926i | 0.00401581i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −52.7114 | −0.281879 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 238.858 | 1.25057 | 0.625283 | − | 0.780398i | \(-0.284984\pi\) | ||||
0.625283 | + | 0.780398i | \(0.284984\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 32.4003i | − | 0.167877i | −0.996471 | − | 0.0839385i | \(-0.973250\pi\) | ||
0.996471 | − | 0.0839385i | \(-0.0267499\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 186.657 | 0.947495 | 0.473748 | − | 0.880661i | \(-0.342901\pi\) | ||||
0.473748 | + | 0.880661i | \(0.342901\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −218.064 | −1.09580 | −0.547899 | − | 0.836545i | \(-0.684572\pi\) | ||||
−0.547899 | + | 0.836545i | \(0.684572\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.9172i | 0.107966i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 0.554700i | − | 0.00270585i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 284.836 | + | 256.411i | 1.36285 | + | 1.22685i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 65.8204i | − | 0.311945i | −0.987761 | − | 0.155973i | \(-0.950149\pi\) | ||
0.987761 | − | 0.155973i | \(-0.0498512\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.860168 | 0.00400078 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 80.5142i | − | 0.371033i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 48.9813i | 0.221635i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.3832i | − | 0.0824358i | −0.999150 | − | 0.0412179i | \(-0.986876\pi\) | ||
0.999150 | − | 0.0412179i | \(-0.0131238\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.7659i | 0.0738586i | 0.999318 | + | 0.0369293i | \(0.0117576\pi\) | ||||
−0.999318 | + | 0.0369293i | \(0.988242\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 126.904 | 0.554165 | 0.277083 | − | 0.960846i | \(-0.410632\pi\) | ||||
0.277083 | + | 0.960846i | \(0.410632\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 286.202 | 1.22834 | 0.614168 | − | 0.789175i | \(-0.289492\pi\) | ||||
0.614168 | + | 0.789175i | \(0.289492\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.962799 | −0.00409702 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 184.163 | 0.770557 | 0.385278 | − | 0.922800i | \(-0.374105\pi\) | ||||
0.385278 | + | 0.922800i | \(0.374105\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.5417i | 0.0561895i | 0.999605 | + | 0.0280948i | \(0.00894402\pi\) | ||||
−0.999605 | + | 0.0280948i | \(0.991056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.237266 | −0.000968433 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 238.266 | − | 264.680i | 0.964640 | − | 1.07158i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 35.0962 | 0.139825 | 0.0699127 | − | 0.997553i | \(-0.477728\pi\) | ||||
0.0699127 | + | 0.997553i | \(0.477728\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −248.579 | −0.982525 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 157.231i | 0.611794i | 0.952065 | + | 0.305897i | \(0.0989564\pi\) | ||||
−0.952065 | + | 0.305897i | \(0.901044\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 337.692i | − | 1.30383i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −268.630 | −1.02141 | −0.510704 | − | 0.859757i | \(-0.670615\pi\) | ||||
−0.510704 | + | 0.859757i | \(0.670615\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.384941i | − | 0.00145261i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 170.930i | − | 0.635426i | −0.948187 | − | 0.317713i | \(-0.897085\pi\) | ||
0.948187 | − | 0.317713i | \(-0.102915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 372.857 | 1.37585 | 0.687927 | − | 0.725779i | \(-0.258521\pi\) | ||||
0.687927 | + | 0.725779i | \(0.258521\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 504.270 | 1.83371 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 400.543 | 1.44600 | 0.723001 | − | 0.690847i | \(-0.242762\pi\) | ||||
0.723001 | + | 0.690847i | \(0.242762\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 149.073i | − | 0.530510i | −0.964178 | − | 0.265255i | \(-0.914544\pi\) | ||
0.964178 | − | 0.265255i | \(-0.0854562\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.4609 | −0.0935013 | −0.0467506 | − | 0.998907i | \(-0.514887\pi\) | ||||
−0.0467506 | + | 0.998907i | \(0.514887\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 252.135i | 0.878520i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −282.171 | −0.976370 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 538.517i | − | 1.83794i | −0.394326 | − | 0.918970i | \(-0.629022\pi\) | ||
0.394326 | − | 0.918970i | \(-0.370978\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 0.580069i | − | 0.00196634i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 230.988i | 0.772536i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −390.984 | −1.29895 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.967174 | 0.00317106 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 284.758i | 0.927552i | 0.885953 | + | 0.463776i | \(0.153506\pi\) | ||||
−0.885953 | + | 0.463776i | \(0.846494\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 128.577 | 0.413431 | 0.206715 | − | 0.978401i | \(-0.433723\pi\) | ||||
0.206715 | + | 0.978401i | \(0.433723\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0647 | 0.0417402 | 0.0208701 | − | 0.999782i | \(-0.493356\pi\) | ||||
0.0208701 | + | 0.999782i | \(0.493356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 238.719i | 0.753056i | 0.926405 | + | 0.376528i | \(0.122882\pi\) | ||||
−0.926405 | + | 0.376528i | \(0.877118\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 82.1520i | 0.257530i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −36.9020 | − | 33.2193i | −0.114248 | − | 0.102846i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 468.585i | − | 1.44180i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 437.634 | 1.33020 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 483.447i | − | 1.46057i | −0.683144 | − | 0.730283i | \(-0.739388\pi\) | ||
0.683144 | − | 0.730283i | \(-0.260612\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 0.767558i | − | 0.00229122i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 238.148i | − | 0.706670i | −0.935497 | − | 0.353335i | \(-0.885048\pi\) | ||
0.935497 | − | 0.353335i | \(-0.114952\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 301.791i | − | 0.885016i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 371.534 | 1.08319 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 283.931 | 0.818244 | 0.409122 | − | 0.912480i | \(-0.365835\pi\) | ||||
0.409122 | + | 0.912480i | \(0.365835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −125.357 | −0.359189 | −0.179595 | − | 0.983741i | \(-0.557479\pi\) | ||||
−0.179595 | + | 0.983741i | \(0.557479\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −134.945 | −0.382281 | −0.191140 | − | 0.981563i | \(-0.561219\pi\) | ||||
−0.191140 | + | 0.981563i | \(0.561219\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 0.221488i | − | 0.000623911i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −434.019 | −1.20897 | −0.604484 | − | 0.796617i | \(-0.706621\pi\) | ||||
−0.604484 | + | 0.796617i | \(0.706621\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.8139 | + | 359.014i | 0.104748 | + | 0.994499i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.39115 | 0.00381137 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 190.842 | 0.520005 | 0.260002 | − | 0.965608i | \(-0.416277\pi\) | ||||
0.260002 | + | 0.965608i | \(0.416277\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 174.973i | 0.471624i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 628.473i | − | 1.68491i | −0.538763 | − | 0.842457i | \(-0.681108\pi\) | ||
0.538763 | − | 0.842457i | \(-0.318892\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 76.3385 | 0.202489 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 296.275i | − | 0.781727i | −0.920449 | − | 0.390864i | \(-0.872176\pi\) | ||
0.920449 | − | 0.390864i | \(-0.127824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 442.460i | 1.15525i | 0.816303 | + | 0.577623i | \(0.196020\pi\) | ||||
−0.816303 | + | 0.577623i | \(0.803980\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.28509 | 0.00333789 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 266.272 | 0.684505 | 0.342253 | − | 0.939608i | \(-0.388810\pi\) | ||||
0.342253 | + | 0.939608i | \(0.388810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.2046 | 0.0823648 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.948371i | 0.00240094i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −198.584 | −0.500211 | −0.250106 | − | 0.968219i | \(-0.580465\pi\) | ||||
−0.250106 | + | 0.968219i | \(0.580465\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 219.350i | − | 0.547007i | −0.961871 | − | 0.273503i | \(-0.911818\pi\) | ||
0.961871 | − | 0.273503i | \(-0.0881825\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −280.434 | −0.695867 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1265.77i | − | 3.11000i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 73.0707i | − | 0.178657i | −0.996002 | − | 0.0893285i | \(-0.971528\pi\) | ||
0.996002 | − | 0.0893285i | \(-0.0284721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 263.667i | 0.638418i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.722617 | 0.00174125 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −130.721 | −0.311983 | −0.155991 | − | 0.987758i | \(-0.549857\pi\) | ||||
−0.155991 | + | 0.987758i | \(0.549857\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 205.731i | − | 0.488673i | −0.969690 | − | 0.244337i | \(-0.921430\pi\) | ||
0.969690 | − | 0.244337i | \(-0.0785702\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −65.3307 | −0.153719 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −439.623 | −1.02956 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 346.636i | 0.804259i | 0.915583 | + | 0.402129i | \(0.131730\pi\) | ||||
−0.915583 | + | 0.402129i | \(0.868270\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 44.3462i | − | 0.102416i | −0.998688 | − | 0.0512081i | \(-0.983693\pi\) | ||
0.998688 | − | 0.0512081i | \(-0.0163072\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −174.024 | − | 156.657i | −0.398224 | − | 0.358483i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 227.421i | 0.518043i | 0.965872 | + | 0.259021i | \(0.0834000\pi\) | ||||
−0.965872 | + | 0.259021i | \(0.916600\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −390.532 | −0.881563 | −0.440782 | − | 0.897614i | \(-0.645299\pi\) | ||||
−0.440782 | + | 0.897614i | \(0.645299\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.57032i | 0.00352880i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 366.375i | 0.815980i | 0.912986 | + | 0.407990i | \(0.133770\pi\) | ||||
−0.912986 | + | 0.407990i | \(0.866230\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 945.077i | 2.09551i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.19415i | − | 0.00262451i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −152.655 | −0.334038 | −0.167019 | − | 0.985954i | \(-0.553414\pi\) | ||||
−0.167019 | + | 0.985954i | \(0.553414\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 295.846 | 0.641749 | 0.320874 | − | 0.947122i | \(-0.396023\pi\) | ||||
0.320874 | + | 0.947122i | \(0.396023\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 596.448 | 1.28822 | 0.644112 | − | 0.764931i | \(-0.277227\pi\) | ||||
0.644112 | + | 0.764931i | \(0.277227\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 795.094 | 1.70256 | 0.851278 | − | 0.524715i | \(-0.175828\pi\) | ||||
0.851278 | + | 0.524715i | \(0.175828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 348.889i | 0.743899i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1465.52 | −3.09836 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 353.027 | + | 317.796i | 0.743214 | + | 0.669045i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 258.081 | 0.538791 | 0.269396 | − | 0.963030i | \(-0.413176\pi\) | ||||
0.269396 | + | 0.963030i | \(0.413176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1176.20 | −2.44531 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.08717i | 0.00224159i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 608.037i | 1.24854i | 0.781210 | + | 0.624268i | \(0.214603\pi\) | ||||
−0.781210 | + | 0.624268i | \(0.785397\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 503.753 | 1.02597 | 0.512987 | − | 0.858396i | \(-0.328539\pi\) | ||||
0.512987 | + | 0.858396i | \(0.328539\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 10.6432i | − | 0.0215886i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 100.676i | 0.202568i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 485.555 | 0.973056 | 0.486528 | − | 0.873665i | \(-0.338263\pi\) | ||||
0.486528 | + | 0.873665i | \(0.338263\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 389.683 | 0.774718 | 0.387359 | − | 0.921929i | \(-0.373387\pi\) | ||||
0.387359 | + | 0.921929i | \(0.373387\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.0494945 | 9.80089e−5 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 361.385i | − | 0.709990i | −0.934868 | − | 0.354995i | \(-0.884483\pi\) | ||
0.934868 | − | 0.354995i | \(-0.115517\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −632.339 | −1.23745 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 0.580615i | − | 0.00112741i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1640.38 | 3.17288 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 798.564i | − | 1.53275i | −0.642392 | − | 0.766377i | \(-0.722058\pi\) | ||
0.642392 | − | 0.766377i | \(-0.277942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 346.310i | − | 0.662160i | −0.943603 | − | 0.331080i | \(-0.892587\pi\) | ||
0.943603 | − | 0.331080i | \(-0.107413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.0985i | 0.0741907i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −377.128 | −0.712907 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 878.199 | 1.64765 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.45717i | − | 0.00272368i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 404.245 | 0.749990 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.91567 | −0.0164800 | −0.00823999 | − | 0.999966i | \(-0.502623\pi\) | ||||
−0.00823999 | + | 0.999966i | \(0.502623\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 0.482589i | − | 0.000885484i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 412.090i | − | 0.753363i | −0.926343 | − | 0.376681i | \(-0.877065\pi\) | ||
0.926343 | − | 0.376681i | \(-0.122935\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.7731 | + | 57.5126i | −0.0939620 | + | 0.104379i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 431.076i | − | 0.779522i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −164.634 | −0.295573 | −0.147786 | − | 0.989019i | \(-0.547215\pi\) | ||||
−0.147786 | + | 0.989019i | \(0.547215\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1361.81i | 2.43616i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 863.263i | 1.53333i | 0.642050 | + | 0.766663i | \(0.278084\pi\) | ||||
−0.642050 | + | 0.766663i | \(0.721916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.23296i | − | 0.00395214i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 635.576i | 1.11700i | 0.829503 | + | 0.558502i | \(0.188624\pi\) | ||||
−0.829503 | + | 0.558502i | \(0.811376\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 111.520 | 0.195306 | 0.0976530 | − | 0.995221i | \(-0.468866\pi\) | ||||
0.0976530 | + | 0.995221i | \(0.468866\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −308.089 | −0.535807 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 658.831 | 1.14182 | 0.570911 | − | 0.821012i | \(-0.306590\pi\) | ||||
0.570911 | + | 0.821012i | \(0.306590\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −328.461 | −0.565337 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 655.849i | 1.12495i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −608.235 | −1.03618 | −0.518088 | − | 0.855327i | \(-0.673356\pi\) | ||||
−0.518088 | + | 0.855327i | \(0.673356\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 190.192 | − | 211.276i | 0.322906 | − | 0.358703i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1086.74 | −1.83261 | −0.916305 | − | 0.400481i | \(-0.868843\pi\) | ||||
−0.916305 | + | 0.400481i | \(0.868843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.166490 | −0.000279815 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 420.739i | 0.702402i | 0.936300 | + | 0.351201i | \(0.114227\pi\) | ||||
−0.936300 | + | 0.351201i | \(0.885773\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 577.036i | − | 0.960126i | −0.877234 | − | 0.480063i | \(-0.840614\pi\) | ||
0.877234 | − | 0.480063i | \(-0.159386\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.38437 | 0.00559400 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 150.995i | − | 0.248756i | −0.992235 | − | 0.124378i | \(-0.960306\pi\) | ||
0.992235 | − | 0.124378i | \(-0.0396935\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1524.30i | − | 2.49476i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −451.848 | −0.737109 | −0.368554 | − | 0.929606i | \(-0.620147\pi\) | ||||
−0.368554 | + | 0.929606i | \(0.620147\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −528.451 | −0.856485 | −0.428242 | − | 0.903664i | \(-0.640867\pi\) | ||||
−0.428242 | + | 0.903664i | \(0.640867\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 63.6940 | 0.102898 | 0.0514491 | − | 0.998676i | \(-0.483616\pi\) | ||||
0.0514491 | + | 0.998676i | \(0.483616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 713.777i | − | 1.14571i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 624.989 | 0.999983 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 163.987i | 0.260710i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −773.865 | −1.22641 | −0.613206 | − | 0.789923i | \(-0.710120\pi\) | ||||
−0.613206 | + | 0.789923i | \(0.710120\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 2.23967i | − | 0.00352703i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 375.638i | − | 0.589699i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 5.28345i | − | 0.00824252i | −0.999992 | − | 0.00412126i | \(-0.998688\pi\) | ||
0.999992 | − | 0.00412126i | \(-0.00131184\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 694.339 | 1.07984 | 0.539922 | − | 0.841715i | \(-0.318454\pi\) | ||||
0.539922 | + | 0.841715i | \(0.318454\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −279.022 | −0.431256 | −0.215628 | − | 0.976476i | \(-0.569180\pi\) | ||||
−0.215628 | + | 0.976476i | \(0.569180\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 988.300i | 1.52280i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −421.633 | −0.645686 | −0.322843 | − | 0.946453i | \(-0.604639\pi\) | ||||
−0.322843 | + | 0.946453i | \(0.604639\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.683880 | 0.00104409 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 376.000i | − | 0.570561i | −0.958444 | − | 0.285280i | \(-0.907913\pi\) | ||
0.958444 | − | 0.285280i | \(-0.0920867\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 720.200i | 1.08956i | 0.838579 | + | 0.544781i | \(0.183387\pi\) | ||||
−0.838579 | + | 0.544781i | \(0.816613\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.899660 | + | 0.809878i | 0.00135287 | + | 0.00121786i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 50.1917i | − | 0.0752499i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1647.84 | −2.45579 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 868.848i | 1.29101i | 0.763757 | + | 0.645504i | \(0.223353\pi\) | ||||
−0.763757 | + | 0.645504i | \(0.776647\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 977.114i | − | 1.44330i | −0.692258 | − | 0.721650i | \(-0.743384\pi\) | ||
0.692258 | − | 0.721650i | \(-0.256616\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 494.167i | − | 0.727786i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 228.420i | − | 0.334437i | −0.985920 | − | 0.167218i | \(-0.946521\pi\) | ||
0.985920 | − | 0.167218i | \(-0.0534785\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.25258 | −0.00328844 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 609.437 | 0.884525 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −94.8120 | −0.137210 | −0.0686049 | − | 0.997644i | \(-0.521855\pi\) | ||||
−0.0686049 | + | 0.997644i | \(0.521855\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.709273 | −0.00102054 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 122.439i | − | 0.175666i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 828.374 | 1.18170 | 0.590852 | − | 0.806780i | \(-0.298792\pi\) | ||||
0.590852 | + | 0.806780i | \(0.298792\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 797.701 | − | 886.134i | 1.13471 | − | 1.26050i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.4974 | −0.0318209 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −475.081 | −0.670073 | −0.335036 | − | 0.942205i | \(-0.608749\pi\) | ||||
−0.335036 | + | 0.942205i | \(0.608749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 184.382i | 0.258601i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4.47602i | − | 0.00626017i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1015.22 | −1.41199 | −0.705997 | − | 0.708215i | \(-0.749501\pi\) | ||||
−0.705997 | + | 0.708215i | \(0.749501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 263.915i | 0.366040i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 101.819i | 0.140440i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.82363 | 0.0107615 | 0.00538076 | − | 0.999986i | \(-0.498287\pi\) | ||||
0.00538076 | + | 0.999986i | \(0.498287\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 189.866 | 0.259734 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 168.524 | 0.229910 | 0.114955 | − | 0.993371i | \(-0.463328\pi\) | ||||
0.114955 | + | 0.993371i | \(0.463328\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1307.74i | 1.77441i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −256.826 | −0.347531 | −0.173766 | − | 0.984787i | \(-0.555594\pi\) | ||||
−0.173766 | + | 0.984787i | \(0.555594\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 848.220i | 1.14161i | 0.821084 | + | 0.570807i | \(0.193370\pi\) | ||||
−0.821084 | + | 0.570807i | \(0.806630\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.49247 | 0.00200331 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 662.348i | 0.884310i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 61.3237i | 0.0816560i | 0.999166 | + | 0.0408280i | \(0.0129996\pi\) | ||||
−0.999166 | + | 0.0408280i | \(0.987000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.02424i | 0.00400561i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −275.977 | −0.364566 | −0.182283 | − | 0.983246i | \(-0.558349\pi\) | ||||
−0.182283 | + | 0.983246i | \(0.558349\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1142.17 | −1.50088 | −0.750441 | − | 0.660938i | \(-0.770159\pi\) | ||||
−0.750441 | + | 0.660938i | \(0.770159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 219.358i | 0.287494i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 918.362 | 1.19734 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −71.7054 | −0.0932450 | −0.0466225 | − | 0.998913i | \(-0.514846\pi\) | ||||
−0.0466225 | + | 0.998913i | \(0.514846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 744.760i | − | 0.963467i | −0.876318 | − | 0.481734i | \(-0.840007\pi\) | ||
0.876318 | − | 0.481734i | \(-0.159993\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 374.040i | − | 0.482632i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −595.598 | + | 661.625i | −0.764567 | + | 0.849326i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 377.364i | 0.483180i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.627173 | 0.000798947 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 426.395i | 0.541797i | 0.962608 | + | 0.270899i | \(0.0873209\pi\) | ||||
−0.962608 | + | 0.270899i | \(0.912679\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1014.98i | 1.28316i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1531.23i | 1.93093i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 490.997i | 0.616056i | 0.951377 | + | 0.308028i | \(0.0996691\pi\) | ||||
−0.951377 | + | 0.308028i | \(0.900331\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −212.520 | −0.265982 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2370.19 | −2.95167 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.785140 | −0.000975329 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1223.89 | −1.51284 | −0.756420 | − | 0.654087i | \(-0.773053\pi\) | ||||
−0.756420 | + | 0.654087i | \(0.773053\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 590.727i | − | 0.728393i | −0.931322 | − | 0.364197i | \(-0.881344\pi\) | ||
0.931322 | − | 0.364197i | \(-0.118656\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.08308 | −0.00378292 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1025.98 | − | 923.588i | −1.25578 | − | 1.13046i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −188.273 | −0.229321 | −0.114661 | − | 0.993405i | \(-0.536578\pi\) | ||||
−0.114661 | + | 0.993405i | \(0.536578\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1419.13 | −1.72434 | −0.862168 | − | 0.506623i | \(-0.830894\pi\) | ||||
−0.862168 | + | 0.506623i | \(0.830894\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1005.56i | 1.21591i | 0.793972 | + | 0.607954i | \(0.208009\pi\) | ||||
−0.793972 | + | 0.607954i | \(0.791991\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 280.910i | − | 0.338854i | −0.985543 | − | 0.169427i | \(-0.945808\pi\) | ||
0.985543 | − | 0.169427i | \(-0.0541917\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −52.3719 | −0.0628715 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.35230i | − | 0.00401473i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 351.194i | 0.418586i | 0.977853 | + | 0.209293i | \(0.0671163\pi\) | ||||
−0.977853 | + | 0.209293i | \(0.932884\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 824.412 | 0.980276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.15848 | −0.00255441 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1538.34 | −1.81623 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 773.336i | 0.908737i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −341.736 | −0.400628 | −0.200314 | − | 0.979732i | \(-0.564196\pi\) | ||||
−0.200314 | + | 0.979732i | \(0.564196\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 738.972i | 0.862278i | 0.902286 | + | 0.431139i | \(0.141888\pi\) | ||||
−0.902286 | + | 0.431139i | \(0.858112\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 375.173 | 0.436756 | 0.218378 | − | 0.975864i | \(-0.429923\pi\) | ||||
0.218378 | + | 0.975864i | \(0.429923\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 195.029i | − | 0.225989i | −0.993596 | − | 0.112995i | \(-0.963956\pi\) | ||
0.993596 | − | 0.112995i | \(-0.0360443\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 1.15039i | − | 0.00132994i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1615.80i | − | 1.85938i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1215.19 | 1.39517 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.18549 | 0.00364057 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1744.13i | 1.98874i | 0.105952 | + | 0.994371i | \(0.466211\pi\) | ||||
−0.105952 | + | 0.994371i | \(0.533789\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 387.876 | 0.440267 | 0.220134 | − | 0.975470i | \(-0.429351\pi\) | ||||
0.220134 | + | 0.975470i | \(0.429351\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −348.266 | −0.394413 | −0.197206 | − | 0.980362i | \(-0.563187\pi\) | ||||
−0.197206 | + | 0.980362i | \(0.563187\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1499.32i | 1.69032i | 0.534510 | + | 0.845162i | \(0.320496\pi\) | ||||
−0.534510 | + | 0.845162i | \(0.679504\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1018.03i | 1.14514i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1148.39 | + | 1033.79i | 1.28599 | + | 1.15766i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.66009i | 0.00408949i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 60.9359 | 0.0677818 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 84.9685i | − | 0.0943046i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 0.742650i | − | 0.000820608i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1270.98i | 1.40130i | 0.713505 | + | 0.700650i | \(0.247107\pi\) | ||||
−0.713505 | + | 0.700650i | \(0.752893\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1691.31i | − | 1.85654i | −0.371910 | − | 0.928269i | \(-0.621297\pi\) | ||
0.371910 | − | 0.928269i | \(-0.378703\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1231.17 | −1.34849 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −310.854 | −0.338990 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −803.862 | −0.874713 | −0.437357 | − | 0.899288i | \(-0.644085\pi\) | ||||
−0.437357 | + | 0.899288i | \(0.644085\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 350.660 | 0.379913 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1568.80i | − | 1.69600i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 818.827 | 0.881407 | 0.440703 | − | 0.897653i | \(-0.354729\pi\) | ||||
0.440703 | + | 0.897653i | \(0.354729\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 283.002 | + | 254.760i | 0.303976 | + | 0.273641i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.624052 | −0.000667436 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −298.683 | −0.318765 | −0.159383 | − | 0.987217i | \(-0.550950\pi\) | ||||
−0.159383 | + | 0.987217i | \(0.550950\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 416.099i | − | 0.442188i | −0.975253 | − | 0.221094i | \(-0.929037\pi\) | ||
0.975253 | − | 0.221094i | \(-0.0709627\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 577.405i | − | 0.612307i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −700.253 | −0.739444 | −0.369722 | − | 0.929142i | \(-0.620547\pi\) | ||||
−0.369722 | + | 0.929142i | \(0.620547\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2202.47i | 2.32083i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 264.222i | 0.277253i | 0.990345 | + | 0.138627i | \(0.0442688\pi\) | ||||
−0.990345 | + | 0.138627i | \(0.955731\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.82785 | 0.00296110 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1023.90 | 1.06767 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 737.148 | 0.767064 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 0.383588i | − | 0.000397500i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 275.678 | 0.285086 | 0.142543 | − | 0.989789i | \(-0.454472\pi\) | ||||
0.142543 | + | 0.989789i | \(0.454472\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1535.48i | − | 1.58133i | −0.612246 | − | 0.790667i | \(-0.709734\pi\) | ||
0.612246 | − | 0.790667i | \(-0.290266\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 322.395 | 0.331342 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1030.08i | 1.05432i | 0.849765 | + | 0.527162i | \(0.176744\pi\) | ||||
−0.849765 | + | 0.527162i | \(0.823256\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2675.44i | − | 2.73283i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 718.441i | − | 0.730866i | −0.930838 | − | 0.365433i | \(-0.880921\pi\) | ||
0.930838 | − | 0.365433i | \(-0.119079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.20983 | 0.00224349 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 895.377 | 0.905336 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 183.179i | − | 0.184842i | −0.995720 | − | 0.0924211i | \(-0.970539\pi\) | ||
0.995720 | − | 0.0924211i | \(-0.0294606\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.58166 | −0.00259464 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1980.18 | 1.98613 | 0.993067 | − | 0.117549i | \(-0.0375037\pi\) | ||||
0.993067 | + | 0.117549i | \(0.0375037\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.3.o.r.721.10 | 20 | ||
3.2 | odd | 2 | 912.3.o.e.721.6 | 20 | |||
4.3 | odd | 2 | 1368.3.o.c.721.10 | 20 | |||
12.11 | even | 2 | 456.3.o.a.265.16 | yes | 20 | ||
19.18 | odd | 2 | inner | 2736.3.o.r.721.9 | 20 | ||
57.56 | even | 2 | 912.3.o.e.721.16 | 20 | |||
76.75 | even | 2 | 1368.3.o.c.721.9 | 20 | |||
228.227 | odd | 2 | 456.3.o.a.265.6 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.3.o.a.265.6 | ✓ | 20 | 228.227 | odd | 2 | ||
456.3.o.a.265.16 | yes | 20 | 12.11 | even | 2 | ||
912.3.o.e.721.6 | 20 | 3.2 | odd | 2 | |||
912.3.o.e.721.16 | 20 | 57.56 | even | 2 | |||
1368.3.o.c.721.9 | 20 | 76.75 | even | 2 | |||
1368.3.o.c.721.10 | 20 | 4.3 | odd | 2 | |||
2736.3.o.r.721.9 | 20 | 19.18 | odd | 2 | inner | ||
2736.3.o.r.721.10 | 20 | 1.1 | even | 1 | trivial |