Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,3,Mod(55,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("189.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.d (of order \(2\), degree \(1\), 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: | \(5.14987699641\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.2 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.55 |
Dual form | 189.3.d.a.55.1 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.500000 | −0.250000 | − | 0.968246i | \(-0.580431\pi\) | ||||
−0.250000 | + | 0.968246i | \(0.580431\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.00000 | −0.750000 | ||||||||
\(5\) | 1.73205i | 0.346410i | 0.984886 | + | 0.173205i | \(0.0554123\pi\) | ||||
−0.984886 | + | 0.173205i | \(0.944588\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.50000 | − | 6.06218i | −0.500000 | − | 0.866025i | ||||
\(8\) | 7.00000 | 0.875000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.73205i | − | 0.173205i | ||||||
\(11\) | 17.0000 | 1.54545 | 0.772727 | − | 0.634738i | \(-0.218892\pi\) | ||||
0.772727 | + | 0.634738i | \(0.218892\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.3205i | 1.33235i | 0.745797 | + | 0.666173i | \(0.232069\pi\) | ||||
−0.745797 | + | 0.666173i | \(0.767931\pi\) | |||||||
\(14\) | 3.50000 | + | 6.06218i | 0.250000 | + | 0.433013i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | 31.1769i | 1.83394i | 0.398961 | + | 0.916968i | \(0.369371\pi\) | ||||
−0.398961 | + | 0.916968i | \(0.630629\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 20.7846i | − | 1.09393i | −0.837157 | − | 0.546963i | \(-0.815784\pi\) | ||
0.837157 | − | 0.546963i | \(-0.184216\pi\) | |||||||
\(20\) | − | 5.19615i | − | 0.259808i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −17.0000 | −0.772727 | ||||||||
\(23\) | 32.0000 | 1.39130 | 0.695652 | − | 0.718379i | \(-0.255116\pi\) | ||||
0.695652 | + | 0.718379i | \(0.255116\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.0000 | 0.880000 | ||||||||
\(26\) | − | 17.3205i | − | 0.666173i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.5000 | + | 18.1865i | 0.375000 | + | 0.649519i | ||||
\(29\) | 2.00000 | 0.0689655 | 0.0344828 | − | 0.999405i | \(-0.489022\pi\) | ||||
0.0344828 | + | 0.999405i | \(0.489022\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.5167i | 0.726344i | 0.931722 | + | 0.363172i | \(0.118306\pi\) | ||||
−0.931722 | + | 0.363172i | \(0.881694\pi\) | |||||||
\(32\) | −33.0000 | −1.03125 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 31.1769i | − | 0.916968i | ||||||
\(35\) | 10.5000 | − | 6.06218i | 0.300000 | − | 0.173205i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000 | 0.216216 | 0.108108 | − | 0.994139i | \(-0.465521\pi\) | ||||
0.108108 | + | 0.994139i | \(0.465521\pi\) | |||||||
\(38\) | 20.7846i | 0.546963i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.1244i | 0.303109i | ||||||||
\(41\) | − | 13.8564i | − | 0.337961i | −0.985619 | − | 0.168981i | \(-0.945952\pi\) | ||
0.985619 | − | 0.168981i | \(-0.0540475\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26.0000 | 0.604651 | 0.302326 | − | 0.953205i | \(-0.402237\pi\) | ||||
0.302326 | + | 0.953205i | \(0.402237\pi\) | |||||||
\(44\) | −51.0000 | −1.15909 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −32.0000 | −0.695652 | ||||||||
\(47\) | − | 38.1051i | − | 0.810747i | −0.914151 | − | 0.405374i | \(-0.867141\pi\) | ||
0.914151 | − | 0.405374i | \(-0.132859\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.5000 | + | 42.4352i | −0.500000 | + | 0.866025i | ||||
\(50\) | −22.0000 | −0.440000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 51.9615i | − | 0.999260i | ||||||
\(53\) | −1.00000 | −0.0188679 | −0.00943396 | − | 0.999955i | \(-0.503003\pi\) | ||||
−0.00943396 | + | 0.999955i | \(0.503003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 29.4449i | 0.535361i | ||||||||
\(56\) | −24.5000 | − | 42.4352i | −0.437500 | − | 0.757772i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.00000 | −0.0344828 | ||||||||
\(59\) | 90.0666i | 1.52655i | 0.646072 | + | 0.763277i | \(0.276411\pi\) | ||||
−0.646072 | + | 0.763277i | \(0.723589\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 69.2820i | − | 1.13577i | −0.823108 | − | 0.567886i | \(-0.807762\pi\) | ||
0.823108 | − | 0.567886i | \(-0.192238\pi\) | |||||||
\(62\) | − | 22.5167i | − | 0.363172i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 0.203125 | ||||||||
\(65\) | −30.0000 | −0.461538 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −34.0000 | −0.507463 | −0.253731 | − | 0.967275i | \(-0.581658\pi\) | ||||
−0.253731 | + | 0.967275i | \(0.581658\pi\) | |||||||
\(68\) | − | 93.5307i | − | 1.37545i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.5000 | + | 6.06218i | −0.150000 | + | 0.0866025i | ||||
\(71\) | −10.0000 | −0.140845 | −0.0704225 | − | 0.997517i | \(-0.522435\pi\) | ||||
−0.0704225 | + | 0.997517i | \(0.522435\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 57.1577i | − | 0.782982i | −0.920182 | − | 0.391491i | \(-0.871959\pi\) | ||
0.920182 | − | 0.391491i | \(-0.128041\pi\) | |||||||
\(74\) | −8.00000 | −0.108108 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 62.3538i | 0.820445i | ||||||||
\(77\) | −59.5000 | − | 103.057i | −0.772727 | − | 1.33840i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −46.0000 | −0.582278 | −0.291139 | − | 0.956681i | \(-0.594034\pi\) | ||||
−0.291139 | + | 0.956681i | \(0.594034\pi\) | |||||||
\(80\) | 8.66025i | 0.108253i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.8564i | 0.168981i | ||||||||
\(83\) | 102.191i | 1.23122i | 0.788052 | + | 0.615608i | \(0.211090\pi\) | ||||
−0.788052 | + | 0.615608i | \(0.788910\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −54.0000 | −0.635294 | ||||||||
\(86\) | −26.0000 | −0.302326 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 119.000 | 1.35227 | ||||||||
\(89\) | − | 51.9615i | − | 0.583837i | −0.956443 | − | 0.291919i | \(-0.905706\pi\) | ||
0.956443 | − | 0.291919i | \(-0.0942937\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 105.000 | − | 60.6218i | 1.15385 | − | 0.666173i | ||||
\(92\) | −96.0000 | −1.04348 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 38.1051i | 0.405374i | ||||||||
\(95\) | 36.0000 | 0.378947 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 91.7987i | 0.946378i | 0.880961 | + | 0.473189i | \(0.156897\pi\) | ||||
−0.880961 | + | 0.473189i | \(0.843103\pi\) | |||||||
\(98\) | 24.5000 | − | 42.4352i | 0.250000 | − | 0.433013i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −66.0000 | −0.660000 | ||||||||
\(101\) | 122.976i | 1.21758i | 0.793331 | + | 0.608790i | \(0.208345\pi\) | ||||
−0.793331 | + | 0.608790i | \(0.791655\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.92820i | 0.0672641i | 0.999434 | + | 0.0336321i | \(0.0107074\pi\) | ||||
−0.999434 | + | 0.0336321i | \(0.989293\pi\) | |||||||
\(104\) | 121.244i | 1.16580i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | 0.00943396 | ||||||||
\(107\) | 107.000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −88.0000 | −0.807339 | −0.403670 | − | 0.914905i | \(-0.632266\pi\) | ||||
−0.403670 | + | 0.914905i | \(0.632266\pi\) | |||||||
\(110\) | − | 29.4449i | − | 0.267681i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −17.5000 | − | 30.3109i | −0.156250 | − | 0.270633i | ||||
\(113\) | 200.000 | 1.76991 | 0.884956 | − | 0.465675i | \(-0.154188\pi\) | ||||
0.884956 | + | 0.465675i | \(0.154188\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 55.4256i | 0.481962i | ||||||||
\(116\) | −6.00000 | −0.0517241 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 90.0666i | − | 0.763277i | ||||||
\(119\) | 189.000 | − | 109.119i | 1.58824 | − | 0.916968i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 168.000 | 1.38843 | ||||||||
\(122\) | 69.2820i | 0.567886i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 67.5500i | − | 0.544758i | ||||||
\(125\) | 81.4064i | 0.651251i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 143.000 | 1.12598 | 0.562992 | − | 0.826462i | \(-0.309650\pi\) | ||||
0.562992 | + | 0.826462i | \(0.309650\pi\) | |||||||
\(128\) | 119.000 | 0.929688 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 30.0000 | 0.230769 | ||||||||
\(131\) | 12.1244i | 0.0925523i | 0.998929 | + | 0.0462762i | \(0.0147354\pi\) | ||||
−0.998929 | + | 0.0462762i | \(0.985265\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −126.000 | + | 72.7461i | −0.947368 | + | 0.546963i | ||||
\(134\) | 34.0000 | 0.253731 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 218.238i | 1.60469i | ||||||||
\(137\) | −10.0000 | −0.0729927 | −0.0364964 | − | 0.999334i | \(-0.511620\pi\) | ||||
−0.0364964 | + | 0.999334i | \(0.511620\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 138.564i | − | 0.996864i | −0.866929 | − | 0.498432i | \(-0.833909\pi\) | ||
0.866929 | − | 0.498432i | \(-0.166091\pi\) | |||||||
\(140\) | −31.5000 | + | 18.1865i | −0.225000 | + | 0.129904i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.0000 | 0.0704225 | ||||||||
\(143\) | 294.449i | 2.05908i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.46410i | 0.0238904i | ||||||||
\(146\) | 57.1577i | 0.391491i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −24.0000 | −0.162162 | ||||||||
\(149\) | −79.0000 | −0.530201 | −0.265101 | − | 0.964221i | \(-0.585405\pi\) | ||||
−0.265101 | + | 0.964221i | \(0.585405\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −73.0000 | −0.483444 | −0.241722 | − | 0.970346i | \(-0.577712\pi\) | ||||
−0.241722 | + | 0.970346i | \(0.577712\pi\) | |||||||
\(152\) | − | 145.492i | − | 0.957186i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 59.5000 | + | 103.057i | 0.386364 | + | 0.669201i | ||||
\(155\) | −39.0000 | −0.251613 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 200.918i | − | 1.27973i | −0.768487 | − | 0.639866i | \(-0.778990\pi\) | ||
0.768487 | − | 0.639866i | \(-0.221010\pi\) | |||||||
\(158\) | 46.0000 | 0.291139 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 57.1577i | − | 0.357235i | ||||||
\(161\) | −112.000 | − | 193.990i | −0.695652 | − | 1.20490i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −226.000 | −1.38650 | −0.693252 | − | 0.720696i | \(-0.743823\pi\) | ||||
−0.693252 | + | 0.720696i | \(0.743823\pi\) | |||||||
\(164\) | 41.5692i | 0.253471i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 102.191i | − | 0.615608i | ||||||
\(167\) | − | 86.6025i | − | 0.518578i | −0.965800 | − | 0.259289i | \(-0.916512\pi\) | ||
0.965800 | − | 0.259289i | \(-0.0834882\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −131.000 | −0.775148 | ||||||||
\(170\) | 54.0000 | 0.317647 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −78.0000 | −0.453488 | ||||||||
\(173\) | − | 74.4782i | − | 0.430510i | −0.976558 | − | 0.215255i | \(-0.930942\pi\) | ||
0.976558 | − | 0.215255i | \(-0.0690582\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −77.0000 | − | 133.368i | −0.440000 | − | 0.762102i | ||||
\(176\) | 85.0000 | 0.482955 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 51.9615i | 0.291919i | ||||||||
\(179\) | 119.000 | 0.664804 | 0.332402 | − | 0.943138i | \(-0.392141\pi\) | ||||
0.332402 | + | 0.943138i | \(0.392141\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 62.3538i | 0.344496i | 0.985054 | + | 0.172248i | \(0.0551031\pi\) | ||||
−0.985054 | + | 0.172248i | \(0.944897\pi\) | |||||||
\(182\) | −105.000 | + | 60.6218i | −0.576923 | + | 0.333087i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 224.000 | 1.21739 | ||||||||
\(185\) | 13.8564i | 0.0748995i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 530.008i | 2.83426i | ||||||||
\(188\) | 114.315i | 0.608060i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −36.0000 | −0.189474 | ||||||||
\(191\) | −190.000 | −0.994764 | −0.497382 | − | 0.867532i | \(-0.665705\pi\) | ||||
−0.497382 | + | 0.867532i | \(0.665705\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 311.000 | 1.61140 | 0.805699 | − | 0.592325i | \(-0.201790\pi\) | ||||
0.805699 | + | 0.592325i | \(0.201790\pi\) | |||||||
\(194\) | − | 91.7987i | − | 0.473189i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 73.5000 | − | 127.306i | 0.375000 | − | 0.649519i | ||||
\(197\) | −307.000 | −1.55838 | −0.779188 | − | 0.626791i | \(-0.784368\pi\) | ||||
−0.779188 | + | 0.626791i | \(0.784368\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 254.611i | − | 1.27945i | −0.768602 | − | 0.639727i | \(-0.779047\pi\) | ||
0.768602 | − | 0.639727i | \(-0.220953\pi\) | |||||||
\(200\) | 154.000 | 0.770000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 122.976i | − | 0.608790i | ||||||
\(203\) | −7.00000 | − | 12.1244i | −0.0344828 | − | 0.0597259i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.0000 | 0.117073 | ||||||||
\(206\) | − | 6.92820i | − | 0.0336321i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 86.6025i | 0.416358i | ||||||||
\(209\) | − | 353.338i | − | 1.69061i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −196.000 | −0.928910 | −0.464455 | − | 0.885597i | \(-0.653750\pi\) | ||||
−0.464455 | + | 0.885597i | \(0.653750\pi\) | |||||||
\(212\) | 3.00000 | 0.0141509 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −107.000 | −0.500000 | ||||||||
\(215\) | 45.0333i | 0.209457i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 136.500 | − | 78.8083i | 0.629032 | − | 0.363172i | ||||
\(218\) | 88.0000 | 0.403670 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 88.3346i | − | 0.401521i | ||||||
\(221\) | −540.000 | −2.44344 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 76.2102i | 0.341750i | 0.985293 | + | 0.170875i | \(0.0546594\pi\) | ||||
−0.985293 | + | 0.170875i | \(0.945341\pi\) | |||||||
\(224\) | 115.500 | + | 200.052i | 0.515625 | + | 0.893089i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −200.000 | −0.884956 | ||||||||
\(227\) | 76.2102i | 0.335728i | 0.985810 | + | 0.167864i | \(0.0536869\pi\) | ||||
−0.985810 | + | 0.167864i | \(0.946313\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 24.2487i | − | 0.105890i | −0.998597 | − | 0.0529448i | \(-0.983139\pi\) | ||
0.998597 | − | 0.0529448i | \(-0.0168607\pi\) | |||||||
\(230\) | − | 55.4256i | − | 0.240981i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.0000 | 0.0603448 | ||||||||
\(233\) | −178.000 | −0.763948 | −0.381974 | − | 0.924173i | \(-0.624756\pi\) | ||||
−0.381974 | + | 0.924173i | \(0.624756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 66.0000 | 0.280851 | ||||||||
\(236\) | − | 270.200i | − | 1.14491i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −189.000 | + | 109.119i | −0.794118 | + | 0.458484i | ||||
\(239\) | −88.0000 | −0.368201 | −0.184100 | − | 0.982907i | \(-0.558937\pi\) | ||||
−0.184100 | + | 0.982907i | \(0.558937\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 200.918i | 0.833684i | 0.908979 | + | 0.416842i | \(0.136863\pi\) | ||||
−0.908979 | + | 0.416842i | \(0.863137\pi\) | |||||||
\(242\) | −168.000 | −0.694215 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 207.846i | 0.851828i | ||||||||
\(245\) | −73.5000 | − | 42.4352i | −0.300000 | − | 0.173205i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 360.000 | 1.45749 | ||||||||
\(248\) | 157.617i | 0.635551i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 81.4064i | − | 0.325626i | ||||||
\(251\) | − | 311.769i | − | 1.24211i | −0.783768 | − | 0.621054i | \(-0.786705\pi\) | ||
0.783768 | − | 0.621054i | \(-0.213295\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 544.000 | 2.15020 | ||||||||
\(254\) | −143.000 | −0.562992 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | − | 3.46410i | − | 0.0134790i | −0.999977 | − | 0.00673950i | \(-0.997855\pi\) | ||
0.999977 | − | 0.00673950i | \(-0.00214526\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.0000 | − | 48.4974i | −0.108108 | − | 0.187249i | ||||
\(260\) | 90.0000 | 0.346154 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 12.1244i | − | 0.0462762i | ||||||
\(263\) | 116.000 | 0.441065 | 0.220532 | − | 0.975380i | \(-0.429221\pi\) | ||||
0.220532 | + | 0.975380i | \(0.429221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.73205i | − | 0.00653604i | ||||||
\(266\) | 126.000 | − | 72.7461i | 0.473684 | − | 0.273482i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 102.000 | 0.380597 | ||||||||
\(269\) | − | 353.338i | − | 1.31353i | −0.754097 | − | 0.656763i | \(-0.771925\pi\) | ||
0.754097 | − | 0.656763i | \(-0.228075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 67.5500i | − | 0.249262i | −0.992203 | − | 0.124631i | \(-0.960225\pi\) | ||
0.992203 | − | 0.124631i | \(-0.0397747\pi\) | |||||||
\(272\) | 155.885i | 0.573105i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000 | 0.0364964 | ||||||||
\(275\) | 374.000 | 1.36000 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −136.000 | −0.490975 | −0.245487 | − | 0.969400i | \(-0.578948\pi\) | ||||
−0.245487 | + | 0.969400i | \(0.578948\pi\) | |||||||
\(278\) | 138.564i | 0.498432i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 73.5000 | − | 42.4352i | 0.262500 | − | 0.151554i | ||||
\(281\) | −370.000 | −1.31673 | −0.658363 | − | 0.752701i | \(-0.728751\pi\) | ||||
−0.658363 | + | 0.752701i | \(0.728751\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 401.836i | 1.41991i | 0.704245 | + | 0.709957i | \(0.251286\pi\) | ||||
−0.704245 | + | 0.709957i | \(0.748714\pi\) | |||||||
\(284\) | 30.0000 | 0.105634 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 294.449i | − | 1.02954i | ||||||
\(287\) | −84.0000 | + | 48.4974i | −0.292683 | + | 0.168981i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −683.000 | −2.36332 | ||||||||
\(290\) | − | 3.46410i | − | 0.0119452i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 171.473i | 0.587236i | ||||||||
\(293\) | 48.4974i | 0.165520i | 0.996569 | + | 0.0827601i | \(0.0263735\pi\) | ||||
−0.996569 | + | 0.0827601i | \(0.973626\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −156.000 | −0.528814 | ||||||||
\(296\) | 56.0000 | 0.189189 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 79.0000 | 0.265101 | ||||||||
\(299\) | 554.256i | 1.85370i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −91.0000 | − | 157.617i | −0.302326 | − | 0.523643i | ||||
\(302\) | 73.0000 | 0.241722 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 103.923i | − | 0.341852i | ||||||
\(305\) | 120.000 | 0.393443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 426.084i | − | 1.38790i | −0.720024 | − | 0.693949i | \(-0.755869\pi\) | ||
0.720024 | − | 0.693949i | \(-0.244131\pi\) | |||||||
\(308\) | 178.500 | + | 309.171i | 0.579545 | + | 1.00380i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 39.0000 | 0.125806 | ||||||||
\(311\) | − | 159.349i | − | 0.512375i | −0.966627 | − | 0.256188i | \(-0.917534\pi\) | ||
0.966627 | − | 0.256188i | \(-0.0824665\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 386.247i | − | 1.23402i | −0.786956 | − | 0.617009i | \(-0.788344\pi\) | ||
0.786956 | − | 0.617009i | \(-0.211656\pi\) | |||||||
\(314\) | 200.918i | 0.639866i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 138.000 | 0.436709 | ||||||||
\(317\) | 227.000 | 0.716088 | 0.358044 | − | 0.933705i | \(-0.383444\pi\) | ||||
0.358044 | + | 0.933705i | \(0.383444\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.0000 | 0.106583 | ||||||||
\(320\) | 22.5167i | 0.0703646i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 112.000 | + | 193.990i | 0.347826 | + | 0.602452i | ||||
\(323\) | 648.000 | 2.00619 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 381.051i | 1.17247i | ||||||||
\(326\) | 226.000 | 0.693252 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 96.9948i | − | 0.295716i | ||||||
\(329\) | −231.000 | + | 133.368i | −0.702128 | + | 0.405374i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 398.000 | 1.20242 | 0.601208 | − | 0.799092i | \(-0.294686\pi\) | ||||
0.601208 | + | 0.799092i | \(0.294686\pi\) | |||||||
\(332\) | − | 306.573i | − | 0.923413i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 86.6025i | 0.259289i | ||||||||
\(335\) | − | 58.8897i | − | 0.175790i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −610.000 | −1.81009 | −0.905045 | − | 0.425317i | \(-0.860163\pi\) | ||||
−0.905045 | + | 0.425317i | \(0.860163\pi\) | |||||||
\(338\) | 131.000 | 0.387574 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 162.000 | 0.476471 | ||||||||
\(341\) | 382.783i | 1.12253i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 1.00000 | ||||||||
\(344\) | 182.000 | 0.529070 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 74.4782i | 0.215255i | ||||||||
\(347\) | 515.000 | 1.48415 | 0.742075 | − | 0.670317i | \(-0.233842\pi\) | ||||
0.742075 | + | 0.670317i | \(0.233842\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 325.626i | 0.933025i | 0.884515 | + | 0.466512i | \(0.154490\pi\) | ||||
−0.884515 | + | 0.466512i | \(0.845510\pi\) | |||||||
\(350\) | 77.0000 | + | 133.368i | 0.220000 | + | 0.381051i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −561.000 | −1.59375 | ||||||||
\(353\) | − | 235.559i | − | 0.667306i | −0.942696 | − | 0.333653i | \(-0.891719\pi\) | ||
0.942696 | − | 0.333653i | \(-0.108281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 17.3205i | − | 0.0487902i | ||||||
\(356\) | 155.885i | 0.437878i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −119.000 | −0.332402 | ||||||||
\(359\) | −226.000 | −0.629526 | −0.314763 | − | 0.949170i | \(-0.601925\pi\) | ||||
−0.314763 | + | 0.949170i | \(0.601925\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −71.0000 | −0.196676 | ||||||||
\(362\) | − | 62.3538i | − | 0.172248i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −315.000 | + | 181.865i | −0.865385 | + | 0.499630i | ||||
\(365\) | 99.0000 | 0.271233 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 531.740i | − | 1.44888i | −0.689337 | − | 0.724441i | \(-0.742098\pi\) | ||
0.689337 | − | 0.724441i | \(-0.257902\pi\) | |||||||
\(368\) | 160.000 | 0.434783 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 13.8564i | − | 0.0374497i | ||||||
\(371\) | 3.50000 | + | 6.06218i | 0.00943396 | + | 0.0163401i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 218.000 | 0.584450 | 0.292225 | − | 0.956350i | \(-0.405604\pi\) | ||||
0.292225 | + | 0.956350i | \(0.405604\pi\) | |||||||
\(374\) | − | 530.008i | − | 1.41713i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 266.736i | − | 0.709404i | ||||||
\(377\) | 34.6410i | 0.0918860i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 296.000 | 0.781003 | 0.390501 | − | 0.920602i | \(-0.372302\pi\) | ||||
0.390501 | + | 0.920602i | \(0.372302\pi\) | |||||||
\(380\) | −108.000 | −0.284211 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 190.000 | 0.497382 | ||||||||
\(383\) | 640.859i | 1.67326i | 0.547768 | + | 0.836630i | \(0.315478\pi\) | ||||
−0.547768 | + | 0.836630i | \(0.684522\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 178.500 | − | 103.057i | 0.463636 | − | 0.267681i | ||||
\(386\) | −311.000 | −0.805699 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 275.396i | − | 0.709784i | ||||||
\(389\) | −457.000 | −1.17481 | −0.587404 | − | 0.809294i | \(-0.699850\pi\) | ||||
−0.587404 | + | 0.809294i | \(0.699850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 997.661i | 2.55156i | ||||||||
\(392\) | −171.500 | + | 297.047i | −0.437500 | + | 0.757772i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 307.000 | 0.779188 | ||||||||
\(395\) | − | 79.6743i | − | 0.201707i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 114.315i | 0.287948i | 0.989581 | + | 0.143974i | \(0.0459882\pi\) | ||||
−0.989581 | + | 0.143974i | \(0.954012\pi\) | |||||||
\(398\) | 254.611i | 0.639727i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 110.000 | 0.275000 | ||||||||
\(401\) | −448.000 | −1.11721 | −0.558603 | − | 0.829435i | \(-0.688663\pi\) | ||||
−0.558603 | + | 0.829435i | \(0.688663\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −390.000 | −0.967742 | ||||||||
\(404\) | − | 368.927i | − | 0.913185i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.00000 | + | 12.1244i | 0.0172414 | + | 0.0298629i | ||||
\(407\) | 136.000 | 0.334152 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 476.314i | − | 1.16458i | −0.812980 | − | 0.582291i | \(-0.802156\pi\) | ||
0.812980 | − | 0.582291i | \(-0.197844\pi\) | |||||||
\(410\) | −24.0000 | −0.0585366 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 20.7846i | − | 0.0504481i | ||||||
\(413\) | 546.000 | − | 315.233i | 1.32203 | − | 0.763277i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −177.000 | −0.426506 | ||||||||
\(416\) | − | 571.577i | − | 1.37398i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 353.338i | 0.845307i | ||||||||
\(419\) | − | 242.487i | − | 0.578728i | −0.957219 | − | 0.289364i | \(-0.906556\pi\) | ||
0.957219 | − | 0.289364i | \(-0.0934438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 548.000 | 1.30166 | 0.650831 | − | 0.759222i | \(-0.274420\pi\) | ||||
0.650831 | + | 0.759222i | \(0.274420\pi\) | |||||||
\(422\) | 196.000 | 0.464455 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.00000 | −0.0165094 | ||||||||
\(425\) | 685.892i | 1.61386i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −420.000 | + | 242.487i | −0.983607 | + | 0.567886i | ||||
\(428\) | −321.000 | −0.750000 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 45.0333i | − | 0.104729i | ||||||
\(431\) | −358.000 | −0.830626 | −0.415313 | − | 0.909678i | \(-0.636328\pi\) | ||||
−0.415313 | + | 0.909678i | \(0.636328\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 161.081i | 0.372011i | 0.982549 | + | 0.186005i | \(0.0595542\pi\) | ||||
−0.982549 | + | 0.186005i | \(0.940446\pi\) | |||||||
\(434\) | −136.500 | + | 78.8083i | −0.314516 | + | 0.181586i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 264.000 | 0.605505 | ||||||||
\(437\) | − | 665.108i | − | 1.52199i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 334.286i | − | 0.761471i | −0.924684 | − | 0.380736i | \(-0.875671\pi\) | ||
0.924684 | − | 0.380736i | \(-0.124329\pi\) | |||||||
\(440\) | 206.114i | 0.468441i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 540.000 | 1.22172 | ||||||||
\(443\) | 650.000 | 1.46727 | 0.733634 | − | 0.679544i | \(-0.237823\pi\) | ||||
0.733634 | + | 0.679544i | \(0.237823\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 90.0000 | 0.202247 | ||||||||
\(446\) | − | 76.2102i | − | 0.170875i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −45.5000 | − | 78.8083i | −0.101562 | − | 0.175911i | ||||
\(449\) | −316.000 | −0.703786 | −0.351893 | − | 0.936040i | \(-0.614462\pi\) | ||||
−0.351893 | + | 0.936040i | \(0.614462\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 235.559i | − | 0.522304i | ||||||
\(452\) | −600.000 | −1.32743 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 76.2102i | − | 0.167864i | ||||||
\(455\) | 105.000 | + | 181.865i | 0.230769 | + | 0.399704i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.0000 | −0.0415755 | −0.0207877 | − | 0.999784i | \(-0.506617\pi\) | ||||
−0.0207877 | + | 0.999784i | \(0.506617\pi\) | |||||||
\(458\) | 24.2487i | 0.0529448i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 166.277i | − | 0.361471i | ||||||
\(461\) | − | 355.070i | − | 0.770218i | −0.922871 | − | 0.385109i | \(-0.874164\pi\) | ||
0.922871 | − | 0.385109i | \(-0.125836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −835.000 | −1.80346 | −0.901728 | − | 0.432304i | \(-0.857701\pi\) | ||||
−0.901728 | + | 0.432304i | \(0.857701\pi\) | |||||||
\(464\) | 10.0000 | 0.0215517 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 178.000 | 0.381974 | ||||||||
\(467\) | 431.281i | 0.923513i | 0.887007 | + | 0.461757i | \(0.152781\pi\) | ||||
−0.887007 | + | 0.461757i | \(0.847219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 119.000 | + | 206.114i | 0.253731 | + | 0.439476i | ||||
\(470\) | −66.0000 | −0.140426 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 630.466i | 1.33573i | ||||||||
\(473\) | 442.000 | 0.934461 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 457.261i | − | 0.962656i | ||||||
\(476\) | −567.000 | + | 327.358i | −1.19118 | + | 0.687726i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 88.0000 | 0.184100 | ||||||||
\(479\) | − | 620.074i | − | 1.29452i | −0.762270 | − | 0.647259i | \(-0.775915\pi\) | ||
0.762270 | − | 0.647259i | \(-0.224085\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 138.564i | 0.288075i | ||||||||
\(482\) | − | 200.918i | − | 0.416842i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −504.000 | −1.04132 | ||||||||
\(485\) | −159.000 | −0.327835 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 98.0000 | 0.201232 | 0.100616 | − | 0.994925i | \(-0.467919\pi\) | ||||
0.100616 | + | 0.994925i | \(0.467919\pi\) | |||||||
\(488\) | − | 484.974i | − | 0.993800i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 73.5000 | + | 42.4352i | 0.150000 | + | 0.0866025i | ||||
\(491\) | −283.000 | −0.576375 | −0.288187 | − | 0.957574i | \(-0.593053\pi\) | ||||
−0.288187 | + | 0.957574i | \(0.593053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 62.3538i | 0.126478i | ||||||||
\(494\) | −360.000 | −0.728745 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 112.583i | 0.226982i | ||||||||
\(497\) | 35.0000 | + | 60.6218i | 0.0704225 | + | 0.121975i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 302.000 | 0.605210 | 0.302605 | − | 0.953116i | \(-0.402144\pi\) | ||||
0.302605 | + | 0.953116i | \(0.402144\pi\) | |||||||
\(500\) | − | 244.219i | − | 0.488438i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 311.769i | 0.621054i | ||||||||
\(503\) | − | 665.108i | − | 1.32228i | −0.750262 | − | 0.661141i | \(-0.770073\pi\) | ||
0.750262 | − | 0.661141i | \(-0.229927\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −213.000 | −0.421782 | ||||||||
\(506\) | −544.000 | −1.07510 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −429.000 | −0.844488 | ||||||||
\(509\) | 583.701i | 1.14676i | 0.819289 | + | 0.573380i | \(0.194368\pi\) | ||||
−0.819289 | + | 0.573380i | \(0.805632\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −346.500 | + | 200.052i | −0.678082 | + | 0.391491i | ||||
\(512\) | −305.000 | −0.595703 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.46410i | 0.00673950i | ||||||||
\(515\) | −12.0000 | −0.0233010 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 647.787i | − | 1.25297i | ||||||
\(518\) | 28.0000 | + | 48.4974i | 0.0540541 | + | 0.0936244i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −210.000 | −0.403846 | ||||||||
\(521\) | − | 280.592i | − | 0.538565i | −0.963061 | − | 0.269282i | \(-0.913214\pi\) | ||
0.963061 | − | 0.269282i | \(-0.0867865\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 966.484i | − | 1.84796i | −0.382438 | − | 0.923981i | \(-0.624915\pi\) | ||
0.382438 | − | 0.923981i | \(-0.375085\pi\) | |||||||
\(524\) | − | 36.3731i | − | 0.0694142i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −116.000 | −0.220532 | ||||||||
\(527\) | −702.000 | −1.33207 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 495.000 | 0.935728 | ||||||||
\(530\) | 1.73205i | 0.00326802i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 378.000 | − | 218.238i | 0.710526 | − | 0.410223i | ||||
\(533\) | 240.000 | 0.450281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 185.329i | 0.346410i | ||||||||
\(536\) | −238.000 | −0.444030 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 353.338i | 0.656763i | ||||||||
\(539\) | −416.500 | + | 721.399i | −0.772727 | + | 1.33840i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −784.000 | −1.44917 | −0.724584 | − | 0.689186i | \(-0.757968\pi\) | ||||
−0.724584 | + | 0.689186i | \(0.757968\pi\) | |||||||
\(542\) | 67.5500i | 0.124631i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 1028.84i | − | 1.89125i | ||||||
\(545\) | − | 152.420i | − | 0.279671i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.0000 | 0.0475320 | 0.0237660 | − | 0.999718i | \(-0.492434\pi\) | ||||
0.0237660 | + | 0.999718i | \(0.492434\pi\) | |||||||
\(548\) | 30.0000 | 0.0547445 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −374.000 | −0.680000 | ||||||||
\(551\) | − | 41.5692i | − | 0.0754432i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 161.000 | + | 278.860i | 0.291139 | + | 0.504268i | ||||
\(554\) | 136.000 | 0.245487 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 415.692i | 0.747648i | ||||||||
\(557\) | 629.000 | 1.12926 | 0.564632 | − | 0.825343i | \(-0.309018\pi\) | ||||
0.564632 | + | 0.825343i | \(0.309018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 450.333i | 0.805605i | ||||||||
\(560\) | 52.5000 | − | 30.3109i | 0.0937500 | − | 0.0541266i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 370.000 | 0.658363 | ||||||||
\(563\) | 874.686i | 1.55362i | 0.629738 | + | 0.776808i | \(0.283162\pi\) | ||||
−0.629738 | + | 0.776808i | \(0.716838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 346.410i | 0.613115i | ||||||||
\(566\) | − | 401.836i | − | 0.709957i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −70.0000 | −0.123239 | ||||||||
\(569\) | 116.000 | 0.203866 | 0.101933 | − | 0.994791i | \(-0.467497\pi\) | ||||
0.101933 | + | 0.994791i | \(0.467497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 590.000 | 1.03327 | 0.516637 | − | 0.856204i | \(-0.327184\pi\) | ||||
0.516637 | + | 0.856204i | \(0.327184\pi\) | |||||||
\(572\) | − | 883.346i | − | 1.54431i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 84.0000 | − | 48.4974i | 0.146341 | − | 0.0844903i | ||||
\(575\) | 704.000 | 1.22435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 270.200i | 0.468284i | 0.972202 | + | 0.234142i | \(0.0752281\pi\) | ||||
−0.972202 | + | 0.234142i | \(0.924772\pi\) | |||||||
\(578\) | 683.000 | 1.18166 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 10.3923i | − | 0.0179178i | ||||||
\(581\) | 619.500 | − | 357.668i | 1.06627 | − | 0.615608i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.0000 | −0.0291595 | ||||||||
\(584\) | − | 400.104i | − | 0.685109i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 48.4974i | − | 0.0827601i | ||||||
\(587\) | 174.937i | 0.298019i | 0.988836 | + | 0.149009i | \(0.0476085\pi\) | ||||
−0.988836 | + | 0.149009i | \(0.952392\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 468.000 | 0.794567 | ||||||||
\(590\) | 156.000 | 0.264407 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 40.0000 | 0.0675676 | ||||||||
\(593\) | 592.361i | 0.998923i | 0.866336 | + | 0.499462i | \(0.166469\pi\) | ||||
−0.866336 | + | 0.499462i | \(0.833531\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 189.000 | + | 327.358i | 0.317647 | + | 0.550181i | ||||
\(596\) | 237.000 | 0.397651 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 554.256i | − | 0.926850i | ||||||
\(599\) | −106.000 | −0.176962 | −0.0884808 | − | 0.996078i | \(-0.528201\pi\) | ||||
−0.0884808 | + | 0.996078i | \(0.528201\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 365.463i | − | 0.608091i | −0.952658 | − | 0.304046i | \(-0.901663\pi\) | ||
0.952658 | − | 0.304046i | \(-0.0983375\pi\) | |||||||
\(602\) | 91.0000 | + | 157.617i | 0.151163 | + | 0.261822i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 219.000 | 0.362583 | ||||||||
\(605\) | 290.985i | 0.480966i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 96.9948i | − | 0.159794i | −0.996803 | − | 0.0798969i | \(-0.974541\pi\) | ||
0.996803 | − | 0.0798969i | \(-0.0254591\pi\) | |||||||
\(608\) | 685.892i | 1.12811i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −120.000 | −0.196721 | ||||||||
\(611\) | 660.000 | 1.08020 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −802.000 | −1.30832 | −0.654160 | − | 0.756356i | \(-0.726978\pi\) | ||||
−0.654160 | + | 0.756356i | \(0.726978\pi\) | |||||||
\(614\) | 426.084i | 0.693949i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −416.500 | − | 721.399i | −0.676136 | − | 1.17110i | ||||
\(617\) | 104.000 | 0.168558 | 0.0842788 | − | 0.996442i | \(-0.473141\pi\) | ||||
0.0842788 | + | 0.996442i | \(0.473141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 523.079i | 0.845039i | 0.906354 | + | 0.422520i | \(0.138854\pi\) | ||||
−0.906354 | + | 0.422520i | \(0.861146\pi\) | |||||||
\(620\) | 117.000 | 0.188710 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 159.349i | 0.256188i | ||||||||
\(623\) | −315.000 | + | 181.865i | −0.505618 | + | 0.291919i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 409.000 | 0.654400 | ||||||||
\(626\) | 386.247i | 0.617009i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 602.754i | 0.959799i | ||||||||
\(629\) | 249.415i | 0.396527i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 767.000 | 1.21553 | 0.607765 | − | 0.794117i | \(-0.292066\pi\) | ||||
0.607765 | + | 0.794117i | \(0.292066\pi\) | |||||||
\(632\) | −322.000 | −0.509494 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −227.000 | −0.358044 | ||||||||
\(635\) | 247.683i | 0.390052i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −735.000 | − | 424.352i | −1.15385 | − | 0.666173i | ||||
\(638\) | −34.0000 | −0.0532915 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 206.114i | 0.322053i | ||||||||
\(641\) | 260.000 | 0.405616 | 0.202808 | − | 0.979218i | \(-0.434993\pi\) | ||||
0.202808 | + | 0.979218i | \(0.434993\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 159.349i | − | 0.247821i | −0.992293 | − | 0.123910i | \(-0.960456\pi\) | ||
0.992293 | − | 0.123910i | \(-0.0395435\pi\) | |||||||
\(644\) | 336.000 | + | 581.969i | 0.521739 | + | 0.903679i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −648.000 | −1.00310 | ||||||||
\(647\) | 519.615i | 0.803115i | 0.915834 | + | 0.401557i | \(0.131531\pi\) | ||||
−0.915834 | + | 0.401557i | \(0.868469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1531.13i | 2.35922i | ||||||||
\(650\) | − | 381.051i | − | 0.586233i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 678.000 | 1.03988 | ||||||||
\(653\) | 1073.00 | 1.64319 | 0.821593 | − | 0.570075i | \(-0.193086\pi\) | ||||
0.821593 | + | 0.570075i | \(0.193086\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.0000 | −0.0320611 | ||||||||
\(656\) | − | 69.2820i | − | 0.105613i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 231.000 | − | 133.368i | 0.351064 | − | 0.202687i | ||||
\(659\) | 503.000 | 0.763278 | 0.381639 | − | 0.924312i | \(-0.375360\pi\) | ||||
0.381639 | + | 0.924312i | \(0.375360\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 990.733i | − | 1.49884i | −0.662095 | − | 0.749420i | \(-0.730333\pi\) | ||
0.662095 | − | 0.749420i | \(-0.269667\pi\) | |||||||
\(662\) | −398.000 | −0.601208 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 715.337i | 1.07731i | ||||||||
\(665\) | −126.000 | − | 218.238i | −0.189474 | − | 0.328178i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 64.0000 | 0.0959520 | ||||||||
\(668\) | 259.808i | 0.388934i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 58.8897i | 0.0878951i | ||||||||
\(671\) | − | 1177.79i | − | 1.75528i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 305.000 | 0.453195 | 0.226597 | − | 0.973989i | \(-0.427240\pi\) | ||||
0.226597 | + | 0.973989i | \(0.427240\pi\) | |||||||
\(674\) | 610.000 | 0.905045 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 393.000 | 0.581361 | ||||||||
\(677\) | − | 6.92820i | − | 0.0102337i | −0.999987 | − | 0.00511684i | \(-0.998371\pi\) | ||
0.999987 | − | 0.00511684i | \(-0.00162875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 556.500 | − | 321.295i | 0.819588 | − | 0.473189i | ||||
\(680\) | −378.000 | −0.555882 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 382.783i | − | 0.561266i | ||||||
\(683\) | −154.000 | −0.225476 | −0.112738 | − | 0.993625i | \(-0.535962\pi\) | ||||
−0.112738 | + | 0.993625i | \(0.535962\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 17.3205i | − | 0.0252854i | ||||||
\(686\) | −343.000 | −0.500000 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 130.000 | 0.188953 | ||||||||
\(689\) | − | 17.3205i | − | 0.0251386i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.8564i | 0.0200527i | 0.999950 | + | 0.0100263i | \(0.00319154\pi\) | ||||
−0.999950 | + | 0.0100263i | \(0.996808\pi\) | |||||||
\(692\) | 223.435i | 0.322882i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −515.000 | −0.742075 | ||||||||
\(695\) | 240.000 | 0.345324 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 432.000 | 0.619799 | ||||||||
\(698\) | − | 325.626i | − | 0.466512i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 231.000 | + | 400.104i | 0.330000 | + | 0.571577i | ||||
\(701\) | −469.000 | −0.669044 | −0.334522 | − | 0.942388i | \(-0.608575\pi\) | ||||
−0.334522 | + | 0.942388i | \(0.608575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 166.277i | − | 0.236525i | ||||||
\(704\) | 221.000 | 0.313920 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 235.559i | 0.333653i | ||||||||
\(707\) | 745.500 | − | 430.415i | 1.05446 | − | 0.608790i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 80.0000 | 0.112835 | 0.0564175 | − | 0.998407i | \(-0.482032\pi\) | ||||
0.0564175 | + | 0.998407i | \(0.482032\pi\) | |||||||
\(710\) | 17.3205i | 0.0243951i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 363.731i | − | 0.510858i | ||||||
\(713\) | 720.533i | 1.01057i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −510.000 | −0.713287 | ||||||||
\(716\) | −357.000 | −0.498603 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 226.000 | 0.314763 | ||||||||
\(719\) | − | 769.031i | − | 1.06958i | −0.844984 | − | 0.534792i | \(-0.820390\pi\) | ||
0.844984 | − | 0.534792i | \(-0.179610\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.0000 | − | 24.2487i | 0.0582524 | − | 0.0336321i | ||||
\(722\) | 71.0000 | 0.0983380 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 187.061i | − | 0.258372i | ||||||
\(725\) | 44.0000 | 0.0606897 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 549.060i | 0.755241i | 0.925960 | + | 0.377620i | \(0.123258\pi\) | ||||
−0.925960 | + | 0.377620i | \(0.876742\pi\) | |||||||
\(728\) | 735.000 | − | 424.352i | 1.00962 | − | 0.582902i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −99.0000 | −0.135616 | ||||||||
\(731\) | 810.600i | 1.10889i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.7128i | 0.0378074i | 0.999821 | + | 0.0189037i | \(0.00601759\pi\) | ||||
−0.999821 | + | 0.0189037i | \(0.993982\pi\) | |||||||
\(734\) | 531.740i | 0.724441i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1056.00 | −1.43478 | ||||||||
\(737\) | −578.000 | −0.784261 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −730.000 | −0.987821 | −0.493911 | − | 0.869513i | \(-0.664433\pi\) | ||||
−0.493911 | + | 0.869513i | \(0.664433\pi\) | |||||||
\(740\) | − | 41.5692i | − | 0.0561746i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.50000 | − | 6.06218i | −0.00471698 | − | 0.00817005i | ||||
\(743\) | −934.000 | −1.25707 | −0.628533 | − | 0.777783i | \(-0.716344\pi\) | ||||
−0.628533 | + | 0.777783i | \(0.716344\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 136.832i | − | 0.183667i | ||||||
\(746\) | −218.000 | −0.292225 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1590.02i | − | 2.12570i | ||||||
\(749\) | −374.500 | − | 648.653i | −0.500000 | − | 0.866025i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −763.000 | −1.01598 | −0.507989 | − | 0.861363i | \(-0.669611\pi\) | ||||
−0.507989 | + | 0.861363i | \(0.669611\pi\) | |||||||
\(752\) | − | 190.526i | − | 0.253358i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 34.6410i | − | 0.0459430i | ||||||
\(755\) | − | 126.440i | − | 0.167470i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −682.000 | −0.900925 | −0.450462 | − | 0.892795i | \(-0.648741\pi\) | ||||
−0.450462 | + | 0.892795i | \(0.648741\pi\) | |||||||
\(758\) | −296.000 | −0.390501 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 252.000 | 0.331579 | ||||||||
\(761\) | 193.990i | 0.254914i | 0.991844 | + | 0.127457i | \(0.0406815\pi\) | ||||
−0.991844 | + | 0.127457i | \(0.959318\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 308.000 | + | 533.472i | 0.403670 | + | 0.699176i | ||||
\(764\) | 570.000 | 0.746073 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 640.859i | − | 0.836630i | ||||||
\(767\) | −1560.00 | −2.03390 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1255.74i | − | 1.63295i | −0.577382 | − | 0.816474i | \(-0.695926\pi\) | ||
0.577382 | − | 0.816474i | \(-0.304074\pi\) | |||||||
\(770\) | −178.500 | + | 103.057i | −0.231818 | + | 0.133840i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −933.000 | −1.20855 | ||||||||
\(773\) | 665.108i | 0.860424i | 0.902728 | + | 0.430212i | \(0.141561\pi\) | ||||
−0.902728 | + | 0.430212i | \(0.858439\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 495.367i | 0.639183i | ||||||||
\(776\) | 642.591i | 0.828081i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 457.000 | 0.587404 | ||||||||
\(779\) | −288.000 | −0.369705 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −170.000 | −0.217670 | ||||||||
\(782\) | − | 997.661i | − | 1.27578i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −122.500 | + | 212.176i | −0.156250 | + | 0.270633i | ||||
\(785\) | 348.000 | 0.443312 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1150.08i | 1.46135i | 0.682726 | + | 0.730675i | \(0.260794\pi\) | ||||
−0.682726 | + | 0.730675i | \(0.739206\pi\) | |||||||
\(788\) | 921.000 | 1.16878 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 79.6743i | 0.100854i | ||||||||
\(791\) | −700.000 | − | 1212.44i | −0.884956 | − | 1.53279i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1200.00 | 1.51324 | ||||||||
\(794\) | − | 114.315i | − | 0.143974i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 763.834i | 0.959591i | ||||||||
\(797\) | 968.216i | 1.21483i | 0.794386 | + | 0.607413i | \(0.207793\pi\) | ||||
−0.794386 | + | 0.607413i | \(0.792207\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1188.00 | 1.48686 | ||||||||
\(800\) | −726.000 | −0.907500 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 448.000 | 0.558603 | ||||||||
\(803\) | − | 971.681i | − | 1.21006i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 336.000 | − | 193.990i | 0.417391 | − | 0.240981i | ||||
\(806\) | 390.000 | 0.483871 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 860.829i | 1.06538i | ||||||||
\(809\) | 638.000 | 0.788628 | 0.394314 | − | 0.918976i | \(-0.370982\pi\) | ||||
0.394314 | + | 0.918976i | \(0.370982\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 581.969i | − | 0.717594i | −0.933416 | − | 0.358797i | \(-0.883187\pi\) | ||
0.933416 | − | 0.358797i | \(-0.116813\pi\) | |||||||
\(812\) | 21.0000 | + | 36.3731i | 0.0258621 | + | 0.0447944i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −136.000 | −0.167076 | ||||||||
\(815\) | − | 391.443i | − | 0.480299i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 540.400i | − | 0.661444i | ||||||
\(818\) | 476.314i | 0.582291i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −72.0000 | −0.0878049 | ||||||||
\(821\) | −262.000 | −0.319123 | −0.159562 | − | 0.987188i | \(-0.551008\pi\) | ||||
−0.159562 | + | 0.987188i | \(0.551008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −769.000 | −0.934386 | −0.467193 | − | 0.884155i | \(-0.654735\pi\) | ||||
−0.467193 | + | 0.884155i | \(0.654735\pi\) | |||||||
\(824\) | 48.4974i | 0.0588561i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −546.000 | + | 315.233i | −0.661017 | + | 0.381638i | ||||
\(827\) | −442.000 | −0.534462 | −0.267231 | − | 0.963633i | \(-0.586109\pi\) | ||||
−0.267231 | + | 0.963633i | \(0.586109\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1340.61i | 1.61714i | 0.588401 | + | 0.808569i | \(0.299757\pi\) | ||||
−0.588401 | + | 0.808569i | \(0.700243\pi\) | |||||||
\(830\) | 177.000 | 0.213253 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 225.167i | 0.270633i | ||||||||
\(833\) | −1323.00 | − | 763.834i | −1.58824 | − | 0.916968i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 150.000 | 0.179641 | ||||||||
\(836\) | 1060.02i | 1.26796i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 242.487i | 0.289364i | ||||||||
\(839\) | − | 1118.90i | − | 1.33362i | −0.745229 | − | 0.666809i | \(-0.767660\pi\) | ||
0.745229 | − | 0.666809i | \(-0.232340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −837.000 | −0.995244 | ||||||||
\(842\) | −548.000 | −0.650831 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 588.000 | 0.696682 | ||||||||
\(845\) | − | 226.899i | − | 0.268519i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −588.000 | − | 1018.45i | −0.694215 | − | 1.20242i | ||||
\(848\) | −5.00000 | −0.00589623 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 685.892i | − | 0.806932i | ||||||
\(851\) | 256.000 | 0.300823 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1077.34i | − | 1.26300i | −0.775377 | − | 0.631498i | \(-0.782440\pi\) | ||
0.775377 | − | 0.631498i | \(-0.217560\pi\) | |||||||
\(854\) | 420.000 | − | 242.487i | 0.491803 | − | 0.283943i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 749.000 | 0.875000 | ||||||||
\(857\) | − | 100.459i | − | 0.117222i | −0.998281 | − | 0.0586108i | \(-0.981333\pi\) | ||
0.998281 | − | 0.0586108i | \(-0.0186671\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 96.9948i | − | 0.112916i | −0.998405 | − | 0.0564580i | \(-0.982019\pi\) | ||
0.998405 | − | 0.0564580i | \(-0.0179807\pi\) | |||||||
\(860\) | − | 135.100i | − | 0.157093i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 358.000 | 0.415313 | ||||||||
\(863\) | −1216.00 | −1.40904 | −0.704519 | − | 0.709685i | \(-0.748837\pi\) | ||||
−0.704519 | + | 0.709685i | \(0.748837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 129.000 | 0.149133 | ||||||||
\(866\) | − | 161.081i | − | 0.186005i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −409.500 | + | 236.425i | −0.471774 | + | 0.272379i | ||||
\(869\) | −782.000 | −0.899885 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 588.897i | − | 0.676116i | ||||||
\(872\) | −616.000 | −0.706422 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 665.108i | 0.760993i | ||||||||
\(875\) | 493.500 | − | 284.922i | 0.564000 | − | 0.325626i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 254.000 | 0.289624 | 0.144812 | − | 0.989459i | \(-0.453742\pi\) | ||||
0.144812 | + | 0.989459i | \(0.453742\pi\) | |||||||
\(878\) | 334.286i | 0.380736i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 147.224i | 0.167300i | ||||||||
\(881\) | 654.715i | 0.743150i | 0.928403 | + | 0.371575i | \(0.121182\pi\) | ||||
−0.928403 | + | 0.371575i | \(0.878818\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 80.0000 | 0.0906002 | 0.0453001 | − | 0.998973i | \(-0.485576\pi\) | ||||
0.0453001 | + | 0.998973i | \(0.485576\pi\) | |||||||
\(884\) | 1620.00 | 1.83258 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −650.000 | −0.733634 | ||||||||
\(887\) | − | 1063.48i | − | 1.19896i | −0.800389 | − | 0.599481i | \(-0.795374\pi\) | ||
0.800389 | − | 0.599481i | \(-0.204626\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −500.500 | − | 866.891i | −0.562992 | − | 0.975131i | ||||
\(890\) | −90.0000 | −0.101124 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 228.631i | − | 0.256312i | ||||||
\(893\) | −792.000 | −0.886898 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 206.114i | 0.230295i | ||||||||
\(896\) | −416.500 | − | 721.399i | −0.464844 | − | 0.805133i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 316.000 | 0.351893 | ||||||||
\(899\) | 45.0333i | 0.0500927i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 31.1769i | − | 0.0346026i | ||||||
\(902\) | 235.559i | 0.261152i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1400.00 | 1.54867 | ||||||||
\(905\) | −108.000 | −0.119337 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −208.000 | −0.229327 | −0.114664 | − | 0.993404i | \(-0.536579\pi\) | ||||
−0.114664 | + | 0.993404i | \(0.536579\pi\) | |||||||
\(908\) | − | 228.631i | − | 0.251796i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −105.000 | − | 181.865i | −0.115385 | − | 0.199852i | ||||
\(911\) | −1654.00 | −1.81559 | −0.907794 | − | 0.419417i | \(-0.862234\pi\) | ||||
−0.907794 | + | 0.419417i | \(0.862234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1737.25i | 1.90279i | ||||||||
\(914\) | 19.0000 | 0.0207877 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 72.7461i | 0.0794172i | ||||||||
\(917\) | 73.5000 | − | 42.4352i | 0.0801527 | − | 0.0462762i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.0000 | 0.0576714 | 0.0288357 | − | 0.999584i | \(-0.490820\pi\) | ||||
0.0288357 | + | 0.999584i | \(0.490820\pi\) | |||||||
\(920\) | 387.979i | 0.421717i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 355.070i | 0.385109i | ||||||||
\(923\) | − | 173.205i | − | 0.187654i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 176.000 | 0.190270 | ||||||||
\(926\) | 835.000 | 0.901728 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −66.0000 | −0.0711207 | ||||||||
\(929\) | − | 297.913i | − | 0.320681i | −0.987062 | − | 0.160341i | \(-0.948741\pi\) | ||
0.987062 | − | 0.160341i | \(-0.0512592\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 882.000 | + | 509.223i | 0.947368 | + | 0.546963i | ||||
\(932\) | 534.000 | 0.572961 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 431.281i | − | 0.461757i | ||||||
\(935\) | −918.000 | −0.981818 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1834.24i | 1.95757i | 0.204893 | + | 0.978784i | \(0.434315\pi\) | ||||
−0.204893 | + | 0.978784i | \(0.565685\pi\) | |||||||
\(938\) | −119.000 | − | 206.114i | −0.126866 | − | 0.219738i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −198.000 | −0.210638 | ||||||||
\(941\) | 1373.52i | 1.45963i | 0.683642 | + | 0.729817i | \(0.260395\pi\) | ||||
−0.683642 | + | 0.729817i | \(0.739605\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 443.405i | − | 0.470207i | ||||||
\(944\) | 450.333i | 0.477048i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −442.000 | −0.467230 | ||||||||
\(947\) | −385.000 | −0.406547 | −0.203273 | − | 0.979122i | \(-0.565158\pi\) | ||||
−0.203273 | + | 0.979122i | \(0.565158\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 990.000 | 1.04320 | ||||||||
\(950\) | 457.261i | 0.481328i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1323.00 | − | 763.834i | 1.38971 | − | 0.802347i | ||||
\(953\) | 1244.00 | 1.30535 | 0.652676 | − | 0.757637i | \(-0.273646\pi\) | ||||
0.652676 | + | 0.757637i | \(0.273646\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 329.090i | − | 0.344596i | ||||||
\(956\) | 264.000 | 0.276151 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 620.074i | 0.647259i | ||||||||
\(959\) | 35.0000 | + | 60.6218i | 0.0364964 | + | 0.0632135i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 454.000 | 0.472425 | ||||||||
\(962\) | − | 138.564i | − | 0.144037i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 602.754i | − | 0.625263i | ||||||
\(965\) | 538.668i | 0.558205i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −535.000 | −0.553257 | −0.276629 | − | 0.960977i | \(-0.589217\pi\) | ||||
−0.276629 | + | 0.960977i | \(0.589217\pi\) | |||||||
\(968\) | 1176.00 | 1.21488 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 159.000 | 0.163918 | ||||||||
\(971\) | 743.050i | 0.765242i | 0.923905 | + | 0.382621i | \(0.124978\pi\) | ||||
−0.923905 | + | 0.382621i | \(0.875022\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −840.000 | + | 484.974i | −0.863309 | + | 0.498432i | ||||
\(974\) | −98.0000 | −0.100616 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 346.410i | − | 0.354928i | ||||||
\(977\) | 950.000 | 0.972364 | 0.486182 | − | 0.873857i | \(-0.338389\pi\) | ||||
0.486182 | + | 0.873857i | \(0.338389\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 883.346i | − | 0.902294i | ||||||
\(980\) | 220.500 | + | 127.306i | 0.225000 | + | 0.129904i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 283.000 | 0.288187 | ||||||||
\(983\) | 1603.88i | 1.63162i | 0.578322 | + | 0.815808i | \(0.303708\pi\) | ||||
−0.578322 | + | 0.815808i | \(0.696292\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 531.740i | − | 0.539837i | ||||||
\(986\) | − | 62.3538i | − | 0.0632392i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1080.00 | −1.09312 | ||||||||
\(989\) | 832.000 | 0.841254 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1151.00 | 1.16145 | 0.580727 | − | 0.814099i | \(-0.302769\pi\) | ||||
0.580727 | + | 0.814099i | \(0.302769\pi\) | |||||||
\(992\) | − | 743.050i | − | 0.749042i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −35.0000 | − | 60.6218i | −0.0352113 | − | 0.0609877i | ||||
\(995\) | 441.000 | 0.443216 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 370.659i | − | 0.371774i | −0.982571 | − | 0.185887i | \(-0.940484\pi\) | ||
0.982571 | − | 0.185887i | \(-0.0595159\pi\) | |||||||
\(998\) | −302.000 | −0.302605 | ||||||||
\(999\) | 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 | 189.3.d.a.55.2 | yes | 2 | |
3.2 | odd | 2 | 189.3.d.c.55.1 | yes | 2 | ||
7.6 | odd | 2 | inner | 189.3.d.a.55.1 | ✓ | 2 | |
21.20 | even | 2 | 189.3.d.c.55.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.3.d.a.55.1 | ✓ | 2 | 7.6 | odd | 2 | inner | |
189.3.d.a.55.2 | yes | 2 | 1.1 | even | 1 | trivial | |
189.3.d.c.55.1 | yes | 2 | 3.2 | odd | 2 | ||
189.3.d.c.55.2 | yes | 2 | 21.20 | even | 2 |