Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (of order \(3\), degree \(2\), 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: | \(52.0396846251\) |
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: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.b.361.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | −7.00000 | + | 12.1244i | −0.626099 | + | 1.08444i | 0.362228 | + | 0.932089i | \(0.382016\pi\) |
−0.988327 | + | 0.152346i | \(0.951317\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −14.0000 | − | 24.2487i | −0.442719 | − | 0.766812i | ||||
\(11\) | −14.0000 | − | 24.2487i | −0.383742 | − | 0.664660i | 0.607852 | − | 0.794050i | \(-0.292031\pi\) |
−0.991594 | + | 0.129390i | \(0.958698\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.0000 | 0.384023 | 0.192012 | − | 0.981393i | \(-0.438499\pi\) | ||||
0.192012 | + | 0.981393i | \(0.438499\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 37.0000 | + | 64.0859i | 0.527872 | + | 0.914301i | 0.999472 | + | 0.0324882i | \(0.0103431\pi\) |
−0.471600 | + | 0.881812i | \(0.656324\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −40.0000 | + | 69.2820i | −0.482980 | + | 0.836547i | −0.999809 | − | 0.0195422i | \(-0.993779\pi\) |
0.516829 | + | 0.856089i | \(0.327112\pi\) | |||||||
\(20\) | 56.0000 | 0.626099 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 56.0000 | 0.542693 | ||||||||
\(23\) | −56.0000 | + | 96.9948i | −0.507687 | + | 0.879340i | 0.492273 | + | 0.870441i | \(0.336166\pi\) |
−0.999960 | + | 0.00889936i | \(0.997167\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −35.5000 | − | 61.4878i | −0.284000 | − | 0.491902i | ||||
\(26\) | −18.0000 | + | 31.1769i | −0.135773 | + | 0.235165i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −190.000 | −1.21662 | −0.608312 | − | 0.793698i | \(-0.708153\pi\) | ||||
−0.608312 | + | 0.793698i | \(0.708153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −36.0000 | − | 62.3538i | −0.208574 | − | 0.361261i | 0.742692 | − | 0.669634i | \(-0.233549\pi\) |
−0.951266 | + | 0.308373i | \(0.900216\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −148.000 | −0.746523 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 173.000 | − | 299.645i | 0.768676 | − | 1.33139i | −0.169605 | − | 0.985512i | \(-0.554249\pi\) |
0.938281 | − | 0.345874i | \(-0.112418\pi\) | |||||||
\(38\) | −80.0000 | − | 138.564i | −0.341519 | − | 0.591528i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −56.0000 | + | 96.9948i | −0.221359 | + | 0.383406i | ||||
\(41\) | −162.000 | −0.617077 | −0.308538 | − | 0.951212i | \(-0.599840\pi\) | ||||
−0.308538 | + | 0.951212i | \(0.599840\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −412.000 | −1.46115 | −0.730575 | − | 0.682833i | \(-0.760748\pi\) | ||||
−0.730575 | + | 0.682833i | \(0.760748\pi\) | |||||||
\(44\) | −56.0000 | + | 96.9948i | −0.191871 | + | 0.332330i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −112.000 | − | 193.990i | −0.358989 | − | 0.621787i | ||||
\(47\) | 12.0000 | − | 20.7846i | 0.0372421 | − | 0.0645053i | −0.846804 | − | 0.531906i | \(-0.821476\pi\) |
0.884046 | + | 0.467401i | \(0.154809\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 142.000 | 0.401637 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −36.0000 | − | 62.3538i | −0.0960058 | − | 0.166287i | ||||
\(53\) | 159.000 | + | 275.396i | 0.412082 | + | 0.713746i | 0.995117 | − | 0.0987002i | \(-0.0314685\pi\) |
−0.583036 | + | 0.812447i | \(0.698135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 392.000 | 0.961041 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 190.000 | − | 329.090i | 0.430142 | − | 0.745027i | ||||
\(59\) | −100.000 | − | 173.205i | −0.220659 | − | 0.382193i | 0.734349 | − | 0.678772i | \(-0.237488\pi\) |
−0.955008 | + | 0.296579i | \(0.904154\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 99.0000 | − | 171.473i | 0.207798 | − | 0.359916i | −0.743223 | − | 0.669044i | \(-0.766704\pi\) |
0.951020 | + | 0.309128i | \(0.100037\pi\) | |||||||
\(62\) | 144.000 | 0.294968 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −126.000 | + | 218.238i | −0.240437 | + | 0.416448i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 358.000 | + | 620.074i | 0.652786 | + | 1.13066i | 0.982444 | + | 0.186558i | \(0.0597332\pi\) |
−0.329658 | + | 0.944100i | \(0.606933\pi\) | |||||||
\(68\) | 148.000 | − | 256.344i | 0.263936 | − | 0.457150i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −392.000 | −0.655237 | −0.327619 | − | 0.944810i | \(-0.606246\pi\) | ||||
−0.327619 | + | 0.944810i | \(0.606246\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −269.000 | − | 465.922i | −0.431289 | − | 0.747014i | 0.565696 | − | 0.824614i | \(-0.308608\pi\) |
−0.996985 | + | 0.0776001i | \(0.975274\pi\) | |||||||
\(74\) | 346.000 | + | 599.290i | 0.543536 | + | 0.941432i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 320.000 | 0.482980 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −120.000 | + | 207.846i | −0.170899 | + | 0.296006i | −0.938735 | − | 0.344641i | \(-0.888001\pi\) |
0.767835 | + | 0.640647i | \(0.221334\pi\) | |||||||
\(80\) | −112.000 | − | 193.990i | −0.156525 | − | 0.271109i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 162.000 | − | 280.592i | 0.218170 | − | 0.377881i | ||||
\(83\) | 1072.00 | 1.41768 | 0.708839 | − | 0.705370i | \(-0.249219\pi\) | ||||
0.708839 | + | 0.705370i | \(0.249219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1036.00 | −1.32200 | ||||||||
\(86\) | 412.000 | − | 713.605i | 0.516594 | − | 0.894767i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −112.000 | − | 193.990i | −0.135673 | − | 0.234993i | ||||
\(89\) | 405.000 | − | 701.481i | 0.482359 | − | 0.835470i | −0.517436 | − | 0.855722i | \(-0.673114\pi\) |
0.999795 | + | 0.0202521i | \(0.00644690\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 448.000 | 0.507687 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 24.0000 | + | 41.5692i | 0.0263342 | + | 0.0456121i | ||||
\(95\) | −560.000 | − | 969.948i | −0.604787 | − | 1.04752i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1354.00 | 1.41730 | 0.708649 | − | 0.705561i | \(-0.249305\pi\) | ||||
0.708649 | + | 0.705561i | \(0.249305\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −142.000 | + | 245.951i | −0.142000 | + | 0.245951i | ||||
\(101\) | −679.000 | − | 1176.06i | −0.668941 | − | 1.15864i | −0.978201 | − | 0.207662i | \(-0.933415\pi\) |
0.309260 | − | 0.950978i | \(-0.399919\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 416.000 | − | 720.533i | 0.397958 | − | 0.689284i | −0.595516 | − | 0.803344i | \(-0.703052\pi\) |
0.993474 | + | 0.114060i | \(0.0363856\pi\) | |||||||
\(104\) | 144.000 | 0.135773 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −636.000 | −0.582772 | ||||||||
\(107\) | 222.000 | − | 384.515i | 0.200575 | − | 0.347406i | −0.748139 | − | 0.663542i | \(-0.769052\pi\) |
0.948714 | + | 0.316136i | \(0.102386\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −935.000 | − | 1619.47i | −0.821622 | − | 1.42309i | −0.904474 | − | 0.426529i | \(-0.859736\pi\) |
0.0828525 | − | 0.996562i | \(-0.473597\pi\) | |||||||
\(110\) | −392.000 | + | 678.964i | −0.339779 | + | 0.588515i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1378.00 | −1.14718 | −0.573590 | − | 0.819143i | \(-0.694450\pi\) | ||||
−0.573590 | + | 0.819143i | \(0.694450\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −784.000 | − | 1357.93i | −0.635725 | − | 1.10111i | ||||
\(116\) | 380.000 | + | 658.179i | 0.304156 | + | 0.526814i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 400.000 | 0.312059 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 273.500 | − | 473.716i | 0.205485 | − | 0.355910i | ||||
\(122\) | 198.000 | + | 342.946i | 0.146935 | + | 0.254499i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −144.000 | + | 249.415i | −0.104287 | + | 0.180630i | ||||
\(125\) | −756.000 | −0.540950 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1944.00 | 1.35828 | 0.679142 | − | 0.734007i | \(-0.262352\pi\) | ||||
0.679142 | + | 0.734007i | \(0.262352\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −252.000 | − | 436.477i | −0.170014 | − | 0.294473i | ||||
\(131\) | −424.000 | + | 734.390i | −0.282787 | + | 0.489801i | −0.972070 | − | 0.234691i | \(-0.924592\pi\) |
0.689283 | + | 0.724492i | \(0.257926\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1432.00 | −0.923179 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 296.000 | + | 512.687i | 0.186631 | + | 0.323254i | ||||
\(137\) | −1483.00 | − | 2568.63i | −0.924827 | − | 1.60185i | −0.791840 | − | 0.610729i | \(-0.790877\pi\) |
−0.132987 | − | 0.991118i | \(-0.542457\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2800.00 | 1.70858 | 0.854291 | − | 0.519795i | \(-0.173992\pi\) | ||||
0.854291 | + | 0.519795i | \(0.173992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 392.000 | − | 678.964i | 0.231661 | − | 0.401249i | ||||
\(143\) | −252.000 | − | 436.477i | −0.147366 | − | 0.255245i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1330.00 | − | 2303.63i | 0.761728 | − | 1.31935i | ||||
\(146\) | 1076.00 | 0.609934 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1384.00 | −0.768676 | ||||||||
\(149\) | 255.000 | − | 441.673i | 0.140204 | − | 0.242841i | −0.787369 | − | 0.616482i | \(-0.788557\pi\) |
0.927573 | + | 0.373641i | \(0.121891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −296.000 | − | 512.687i | −0.159524 | − | 0.276304i | 0.775173 | − | 0.631749i | \(-0.217663\pi\) |
−0.934697 | + | 0.355445i | \(0.884329\pi\) | |||||||
\(152\) | −320.000 | + | 554.256i | −0.170759 | + | 0.295764i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1008.00 | 0.522352 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1343.00 | + | 2326.14i | 0.682695 | + | 1.18246i | 0.974155 | + | 0.225879i | \(0.0725254\pi\) |
−0.291461 | + | 0.956583i | \(0.594141\pi\) | |||||||
\(158\) | −240.000 | − | 415.692i | −0.120844 | − | 0.209308i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 448.000 | 0.221359 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 506.000 | − | 876.418i | 0.243147 | − | 0.421143i | −0.718462 | − | 0.695566i | \(-0.755154\pi\) |
0.961609 | + | 0.274423i | \(0.0884869\pi\) | |||||||
\(164\) | 324.000 | + | 561.184i | 0.154269 | + | 0.267202i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1072.00 | + | 1856.76i | −0.501225 | + | 0.868147i | ||||
\(167\) | −544.000 | −0.252072 | −0.126036 | − | 0.992026i | \(-0.540225\pi\) | ||||
−0.126036 | + | 0.992026i | \(0.540225\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1873.00 | −0.852526 | ||||||||
\(170\) | 1036.00 | − | 1794.40i | 0.467397 | − | 0.809556i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 824.000 | + | 1427.21i | 0.365287 | + | 0.632696i | ||||
\(173\) | 929.000 | − | 1609.08i | 0.408269 | − | 0.707143i | −0.586427 | − | 0.810002i | \(-0.699466\pi\) |
0.994696 | + | 0.102859i | \(0.0327992\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 448.000 | 0.191871 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 810.000 | + | 1402.96i | 0.341079 | + | 0.590766i | ||||
\(179\) | −150.000 | − | 259.808i | −0.0626342 | − | 0.108486i | 0.833008 | − | 0.553261i | \(-0.186617\pi\) |
−0.895642 | + | 0.444775i | \(0.853283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2358.00 | −0.968336 | −0.484168 | − | 0.874975i | \(-0.660878\pi\) | ||||
−0.484168 | + | 0.874975i | \(0.660878\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −448.000 | + | 775.959i | −0.179495 | + | 0.310894i | ||||
\(185\) | 2422.00 | + | 4195.03i | 0.962535 | + | 1.66716i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1036.00 | − | 1794.40i | 0.405133 | − | 0.701710i | ||||
\(188\) | −96.0000 | −0.0372421 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2240.00 | 0.855298 | ||||||||
\(191\) | 696.000 | − | 1205.51i | 0.263669 | − | 0.456688i | −0.703545 | − | 0.710651i | \(-0.748401\pi\) |
0.967214 | + | 0.253962i | \(0.0817340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −889.000 | − | 1539.79i | −0.331563 | − | 0.574284i | 0.651256 | − | 0.758858i | \(-0.274243\pi\) |
−0.982818 | + | 0.184575i | \(0.940909\pi\) | |||||||
\(194\) | −1354.00 | + | 2345.20i | −0.501090 | + | 0.867914i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1214.00 | −0.439055 | −0.219528 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219528 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −520.000 | − | 900.666i | −0.185235 | − | 0.320837i | 0.758420 | − | 0.651766i | \(-0.225971\pi\) |
−0.943656 | + | 0.330929i | \(0.892638\pi\) | |||||||
\(200\) | −284.000 | − | 491.902i | −0.100409 | − | 0.173914i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2716.00 | 0.946025 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1134.00 | − | 1964.15i | 0.386351 | − | 0.669180i | ||||
\(206\) | 832.000 | + | 1441.07i | 0.281399 | + | 0.487397i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −144.000 | + | 249.415i | −0.0480029 | + | 0.0831435i | ||||
\(209\) | 2240.00 | 0.741359 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3868.00 | −1.26201 | −0.631005 | − | 0.775779i | \(-0.717357\pi\) | ||||
−0.631005 | + | 0.775779i | \(0.717357\pi\) | |||||||
\(212\) | 636.000 | − | 1101.58i | 0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 444.000 | + | 769.031i | 0.141828 | + | 0.245653i | ||||
\(215\) | 2884.00 | − | 4995.23i | 0.914824 | − | 1.58452i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3740.00 | 1.16195 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −784.000 | − | 1357.93i | −0.240260 | − | 0.416143i | ||||
\(221\) | 666.000 | + | 1153.55i | 0.202715 | + | 0.351113i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3968.00 | 1.19156 | 0.595778 | − | 0.803149i | \(-0.296844\pi\) | ||||
0.595778 | + | 0.803149i | \(0.296844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1378.00 | − | 2386.77i | 0.405589 | − | 0.702501i | ||||
\(227\) | −1968.00 | − | 3408.68i | −0.575422 | − | 0.996660i | −0.995996 | − | 0.0894015i | \(-0.971505\pi\) |
0.420574 | − | 0.907258i | \(-0.361829\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2405.00 | + | 4165.58i | −0.694004 | + | 1.20205i | 0.276512 | + | 0.961011i | \(0.410822\pi\) |
−0.970515 | + | 0.241039i | \(0.922512\pi\) | |||||||
\(230\) | 3136.00 | 0.899051 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1520.00 | −0.430142 | ||||||||
\(233\) | −1091.00 | + | 1889.67i | −0.306754 | + | 0.531314i | −0.977650 | − | 0.210237i | \(-0.932576\pi\) |
0.670896 | + | 0.741551i | \(0.265910\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 168.000 | + | 290.985i | 0.0466345 | + | 0.0807734i | ||||
\(236\) | −400.000 | + | 692.820i | −0.110330 | + | 0.191096i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3000.00 | 0.811941 | 0.405970 | − | 0.913886i | \(-0.366934\pi\) | ||||
0.405970 | + | 0.913886i | \(0.366934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1021.00 | − | 1768.42i | −0.272898 | − | 0.472673i | 0.696705 | − | 0.717358i | \(-0.254649\pi\) |
−0.969603 | + | 0.244685i | \(0.921315\pi\) | |||||||
\(242\) | 547.000 | + | 947.432i | 0.145300 | + | 0.251666i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −792.000 | −0.207798 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −720.000 | + | 1247.08i | −0.185476 | + | 0.321253i | ||||
\(248\) | −288.000 | − | 498.831i | −0.0737420 | − | 0.127725i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 756.000 | − | 1309.43i | 0.191255 | − | 0.331263i | ||||
\(251\) | 528.000 | 0.132777 | 0.0663886 | − | 0.997794i | \(-0.478852\pi\) | ||||
0.0663886 | + | 0.997794i | \(0.478852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3136.00 | 0.779283 | ||||||||
\(254\) | −1944.00 | + | 3367.11i | −0.480226 | + | 0.831776i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2817.00 | − | 4879.19i | 0.683734 | − | 1.18426i | −0.290099 | − | 0.956997i | \(-0.593688\pi\) |
0.973833 | − | 0.227265i | \(-0.0729785\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1008.00 | 0.240437 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −848.000 | − | 1468.78i | −0.199960 | − | 0.346342i | ||||
\(263\) | 84.0000 | + | 145.492i | 0.0196945 | + | 0.0341119i | 0.875705 | − | 0.482847i | \(-0.160397\pi\) |
−0.856010 | + | 0.516959i | \(0.827064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4452.00 | −1.03202 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1432.00 | − | 2480.30i | 0.326393 | − | 0.565329i | ||||
\(269\) | −655.000 | − | 1134.49i | −0.148461 | − | 0.257142i | 0.782198 | − | 0.623030i | \(-0.214099\pi\) |
−0.930659 | + | 0.365888i | \(0.880765\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1104.00 | − | 1912.18i | 0.247466 | − | 0.428623i | −0.715356 | − | 0.698760i | \(-0.753736\pi\) |
0.962822 | + | 0.270137i | \(0.0870689\pi\) | |||||||
\(272\) | −1184.00 | −0.263936 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5932.00 | 1.30790 | ||||||||
\(275\) | −994.000 | + | 1721.66i | −0.217965 | + | 0.377527i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2647.00 | − | 4584.74i | −0.574162 | − | 0.994477i | −0.996132 | − | 0.0878678i | \(-0.971995\pi\) |
0.421970 | − | 0.906610i | \(-0.361339\pi\) | |||||||
\(278\) | −2800.00 | + | 4849.74i | −0.604075 | + | 1.04629i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3242.00 | −0.688262 | −0.344131 | − | 0.938922i | \(-0.611826\pi\) | ||||
−0.344131 | + | 0.938922i | \(0.611826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 796.000 | + | 1378.71i | 0.167199 | + | 0.289597i | 0.937434 | − | 0.348163i | \(-0.113194\pi\) |
−0.770235 | + | 0.637760i | \(0.779861\pi\) | |||||||
\(284\) | 784.000 | + | 1357.93i | 0.163809 | + | 0.283726i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1008.00 | 0.208407 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −281.500 | + | 487.572i | −0.0572970 | + | 0.0992413i | ||||
\(290\) | 2660.00 | + | 4607.26i | 0.538623 | + | 0.932922i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1076.00 | + | 1863.69i | −0.215644 | + | 0.373507i | ||||
\(293\) | 5022.00 | 1.00133 | 0.500663 | − | 0.865642i | \(-0.333090\pi\) | ||||
0.500663 | + | 0.865642i | \(0.333090\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2800.00 | 0.552618 | ||||||||
\(296\) | 1384.00 | − | 2397.16i | 0.271768 | − | 0.470716i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 510.000 | + | 883.346i | 0.0991393 | + | 0.171714i | ||||
\(299\) | −1008.00 | + | 1745.91i | −0.194964 | + | 0.337687i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1184.00 | 0.225601 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −640.000 | − | 1108.51i | −0.120745 | − | 0.209137i | ||||
\(305\) | 1386.00 | + | 2400.62i | 0.260204 | + | 0.450686i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9536.00 | −1.77280 | −0.886398 | − | 0.462924i | \(-0.846800\pi\) | ||||
−0.886398 | + | 0.462924i | \(0.846800\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1008.00 | + | 1745.91i | −0.184679 | + | 0.319874i | ||||
\(311\) | −484.000 | − | 838.313i | −0.0882480 | − | 0.152850i | 0.818523 | − | 0.574474i | \(-0.194793\pi\) |
−0.906771 | + | 0.421624i | \(0.861460\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1529.00 | + | 2648.31i | −0.276116 | + | 0.478246i | −0.970416 | − | 0.241439i | \(-0.922381\pi\) |
0.694300 | + | 0.719685i | \(0.255714\pi\) | |||||||
\(314\) | −5372.00 | −0.965476 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 960.000 | 0.170899 | ||||||||
\(317\) | −2493.00 | + | 4318.00i | −0.441706 | + | 0.765057i | −0.997816 | − | 0.0660512i | \(-0.978960\pi\) |
0.556110 | + | 0.831109i | \(0.312293\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2660.00 | + | 4607.26i | 0.466870 | + | 0.808642i | ||||
\(320\) | −448.000 | + | 775.959i | −0.0782624 | + | 0.135554i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5920.00 | −1.01981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −639.000 | − | 1106.78i | −0.109063 | − | 0.188902i | ||||
\(326\) | 1012.00 | + | 1752.84i | 0.171931 | + | 0.297793i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1296.00 | −0.218170 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4306.00 | + | 7458.21i | −0.715043 | + | 1.23849i | 0.247900 | + | 0.968786i | \(0.420259\pi\) |
−0.962943 | + | 0.269705i | \(0.913074\pi\) | |||||||
\(332\) | −2144.00 | − | 3713.52i | −0.354420 | − | 0.613873i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 544.000 | − | 942.236i | 0.0891208 | − | 0.154362i | ||||
\(335\) | −10024.0 | −1.63483 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10206.0 | −1.64972 | −0.824861 | − | 0.565336i | \(-0.808747\pi\) | ||||
−0.824861 | + | 0.565336i | \(0.808747\pi\) | |||||||
\(338\) | 1873.00 | − | 3244.13i | 0.301414 | − | 0.522064i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2072.00 | + | 3588.81i | 0.330500 | + | 0.572443i | ||||
\(341\) | −1008.00 | + | 1745.91i | −0.160077 | + | 0.277262i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3296.00 | −0.516594 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1858.00 | + | 3218.15i | 0.288690 | + | 0.500026i | ||||
\(347\) | 1002.00 | + | 1735.51i | 0.155015 | + | 0.268494i | 0.933064 | − | 0.359709i | \(-0.117124\pi\) |
−0.778050 | + | 0.628203i | \(0.783791\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1330.00 | 0.203992 | 0.101996 | − | 0.994785i | \(-0.467477\pi\) | ||||
0.101996 | + | 0.994785i | \(0.467477\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −448.000 | + | 775.959i | −0.0678366 | + | 0.117496i | ||||
\(353\) | 489.000 | + | 846.973i | 0.0737304 | + | 0.127705i | 0.900533 | − | 0.434787i | \(-0.143176\pi\) |
−0.826803 | + | 0.562492i | \(0.809843\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2744.00 | − | 4752.75i | 0.410243 | − | 0.710562i | ||||
\(356\) | −3240.00 | −0.482359 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 600.000 | 0.0885782 | ||||||||
\(359\) | −4840.00 | + | 8383.13i | −0.711547 | + | 1.23244i | 0.252729 | + | 0.967537i | \(0.418672\pi\) |
−0.964276 | + | 0.264899i | \(0.914661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 229.500 | + | 397.506i | 0.0334597 | + | 0.0579539i | ||||
\(362\) | 2358.00 | − | 4084.18i | 0.342358 | − | 0.592982i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7532.00 | 1.08012 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4328.00 | + | 7496.32i | 0.615585 | + | 1.06622i | 0.990282 | + | 0.139077i | \(0.0444136\pi\) |
−0.374696 | + | 0.927148i | \(0.622253\pi\) | |||||||
\(368\) | −896.000 | − | 1551.92i | −0.126922 | − | 0.219835i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9688.00 | −1.36123 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2639.00 | + | 4570.88i | −0.366333 | + | 0.634508i | −0.988989 | − | 0.147988i | \(-0.952720\pi\) |
0.622656 | + | 0.782496i | \(0.286054\pi\) | |||||||
\(374\) | 2072.00 | + | 3588.81i | 0.286472 | + | 0.496184i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 96.0000 | − | 166.277i | 0.0131671 | − | 0.0228061i | ||||
\(377\) | −3420.00 | −0.467212 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6340.00 | 0.859272 | 0.429636 | − | 0.903002i | \(-0.358642\pi\) | ||||
0.429636 | + | 0.903002i | \(0.358642\pi\) | |||||||
\(380\) | −2240.00 | + | 3879.79i | −0.302394 | + | 0.523761i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1392.00 | + | 2411.01i | 0.186442 | + | 0.322927i | ||||
\(383\) | −3116.00 | + | 5397.07i | −0.415718 | + | 0.720045i | −0.995504 | − | 0.0947240i | \(-0.969803\pi\) |
0.579785 | + | 0.814769i | \(0.303136\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3556.00 | 0.468901 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2708.00 | − | 4690.39i | −0.354324 | − | 0.613708i | ||||
\(389\) | −7405.00 | − | 12825.8i | −0.965163 | − | 1.67171i | −0.709177 | − | 0.705031i | \(-0.750933\pi\) |
−0.255986 | − | 0.966680i | \(-0.582400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8288.00 | −1.07197 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1214.00 | − | 2102.71i | 0.155230 | − | 0.268865i | ||||
\(395\) | −1680.00 | − | 2909.85i | −0.214000 | − | 0.370659i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2577.00 | + | 4463.49i | −0.325783 | + | 0.564273i | −0.981671 | − | 0.190586i | \(-0.938961\pi\) |
0.655887 | + | 0.754859i | \(0.272295\pi\) | |||||||
\(398\) | 2080.00 | 0.261962 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1136.00 | 0.142000 | ||||||||
\(401\) | 1641.00 | − | 2842.30i | 0.204358 | − | 0.353959i | −0.745570 | − | 0.666427i | \(-0.767823\pi\) |
0.949928 | + | 0.312469i | \(0.101156\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −648.000 | − | 1122.37i | −0.0800972 | − | 0.138732i | ||||
\(404\) | −2716.00 | + | 4704.25i | −0.334470 | + | 0.579320i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9688.00 | −1.17989 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2905.00 | − | 5031.61i | −0.351205 | − | 0.608306i | 0.635256 | − | 0.772302i | \(-0.280895\pi\) |
−0.986461 | + | 0.163996i | \(0.947561\pi\) | |||||||
\(410\) | 2268.00 | + | 3928.29i | 0.273192 | + | 0.473182i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3328.00 | −0.397958 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7504.00 | + | 12997.3i | −0.887607 | + | 1.53738i | ||||
\(416\) | −288.000 | − | 498.831i | −0.0339432 | − | 0.0587913i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2240.00 | + | 3879.79i | −0.262110 | + | 0.453988i | ||||
\(419\) | −13560.0 | −1.58102 | −0.790512 | − | 0.612446i | \(-0.790186\pi\) | ||||
−0.790512 | + | 0.612446i | \(0.790186\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −738.000 | −0.0854345 | −0.0427172 | − | 0.999087i | \(-0.513601\pi\) | ||||
−0.0427172 | + | 0.999087i | \(0.513601\pi\) | |||||||
\(422\) | 3868.00 | − | 6699.57i | 0.446188 | − | 0.772820i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1272.00 | + | 2203.17i | 0.145693 | + | 0.252347i | ||||
\(425\) | 2627.00 | − | 4550.10i | 0.299831 | − | 0.519323i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1776.00 | −0.200575 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5768.00 | + | 9990.47i | 0.646878 | + | 1.12043i | ||||
\(431\) | 636.000 | + | 1101.58i | 0.0710790 | + | 0.123112i | 0.899374 | − | 0.437179i | \(-0.144022\pi\) |
−0.828295 | + | 0.560292i | \(0.810689\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5062.00 | −0.561811 | −0.280906 | − | 0.959735i | \(-0.590635\pi\) | ||||
−0.280906 | + | 0.959735i | \(0.590635\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3740.00 | + | 6477.87i | −0.410811 | + | 0.711545i | ||||
\(437\) | −4480.00 | − | 7759.59i | −0.490406 | − | 0.849408i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2820.00 | + | 4884.38i | −0.306586 | + | 0.531023i | −0.977613 | − | 0.210410i | \(-0.932520\pi\) |
0.671027 | + | 0.741433i | \(0.265853\pi\) | |||||||
\(440\) | 3136.00 | 0.339779 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2664.00 | −0.286682 | ||||||||
\(443\) | 6694.00 | − | 11594.3i | 0.717927 | − | 1.24349i | −0.243893 | − | 0.969802i | \(-0.578425\pi\) |
0.961820 | − | 0.273683i | \(-0.0882421\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5670.00 | + | 9820.73i | 0.604008 | + | 1.04617i | ||||
\(446\) | −3968.00 | + | 6872.78i | −0.421279 | + | 0.729676i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3230.00 | 0.339495 | 0.169747 | − | 0.985488i | \(-0.445705\pi\) | ||||
0.169747 | + | 0.985488i | \(0.445705\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2268.00 | + | 3928.29i | 0.236798 | + | 0.410146i | ||||
\(452\) | 2756.00 | + | 4773.53i | 0.286795 | + | 0.496743i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7872.00 | 0.813769 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5323.00 | − | 9219.71i | 0.544857 | − | 0.943719i | −0.453759 | − | 0.891124i | \(-0.649917\pi\) |
0.998616 | − | 0.0525950i | \(-0.0167492\pi\) | |||||||
\(458\) | −4810.00 | − | 8331.16i | −0.490735 | − | 0.849978i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3136.00 | + | 5431.71i | −0.317863 | + | 0.550554i | ||||
\(461\) | −7282.00 | −0.735698 | −0.367849 | − | 0.929886i | \(-0.619906\pi\) | ||||
−0.367849 | + | 0.929886i | \(0.619906\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12688.0 | 1.27357 | 0.636783 | − | 0.771043i | \(-0.280265\pi\) | ||||
0.636783 | + | 0.771043i | \(0.280265\pi\) | |||||||
\(464\) | 1520.00 | − | 2632.72i | 0.152078 | − | 0.263407i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2182.00 | − | 3779.33i | −0.216908 | − | 0.375696i | ||||
\(467\) | −1408.00 | + | 2438.73i | −0.139517 | + | 0.241651i | −0.927314 | − | 0.374285i | \(-0.877888\pi\) |
0.787797 | + | 0.615935i | \(0.211222\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −672.000 | −0.0659512 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −800.000 | − | 1385.64i | −0.0780148 | − | 0.135126i | ||||
\(473\) | 5768.00 | + | 9990.47i | 0.560704 | + | 0.971168i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5680.00 | 0.548666 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3000.00 | + | 5196.15i | −0.287064 | + | 0.497210i | ||||
\(479\) | −1580.00 | − | 2736.64i | −0.150714 | − | 0.261044i | 0.780776 | − | 0.624811i | \(-0.214824\pi\) |
−0.931490 | + | 0.363766i | \(0.881491\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3114.00 | − | 5393.61i | 0.295190 | − | 0.511283i | ||||
\(482\) | 4084.00 | 0.385936 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2188.00 | −0.205485 | ||||||||
\(485\) | −9478.00 | + | 16416.4i | −0.887369 | + | 1.53697i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7088.00 | + | 12276.8i | 0.659523 | + | 1.14233i | 0.980739 | + | 0.195322i | \(0.0625752\pi\) |
−0.321216 | + | 0.947006i | \(0.604091\pi\) | |||||||
\(488\) | 792.000 | − | 1371.78i | 0.0734675 | − | 0.127249i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11268.0 | 1.03568 | 0.517839 | − | 0.855478i | \(-0.326737\pi\) | ||||
0.517839 | + | 0.855478i | \(0.326737\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7030.00 | − | 12176.3i | −0.642222 | − | 1.11236i | ||||
\(494\) | −1440.00 | − | 2494.15i | −0.131151 | − | 0.227160i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1152.00 | 0.104287 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2230.00 | − | 3862.47i | 0.200057 | − | 0.346509i | −0.748489 | − | 0.663147i | \(-0.769221\pi\) |
0.948547 | + | 0.316638i | \(0.102554\pi\) | |||||||
\(500\) | 1512.00 | + | 2618.86i | 0.135237 | + | 0.234238i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −528.000 | + | 914.523i | −0.0469438 | + | 0.0813091i | ||||
\(503\) | 1512.00 | 0.134029 | 0.0670147 | − | 0.997752i | \(-0.478653\pi\) | ||||
0.0670147 | + | 0.997752i | \(0.478653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19012.0 | 1.67529 | ||||||||
\(506\) | −3136.00 | + | 5431.71i | −0.275518 | + | 0.477212i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3888.00 | − | 6734.21i | −0.339571 | − | 0.588154i | ||||
\(509\) | −5895.00 | + | 10210.4i | −0.513342 | + | 0.889135i | 0.486538 | + | 0.873660i | \(0.338260\pi\) |
−0.999880 | + | 0.0154756i | \(0.995074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5634.00 | + | 9758.37i | 0.483473 | + | 0.837400i | ||||
\(515\) | 5824.00 | + | 10087.5i | 0.498323 | + | 0.863120i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −672.000 | −0.0571654 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1008.00 | + | 1745.91i | −0.0850072 | + | 0.147237i | ||||
\(521\) | 681.000 | + | 1179.53i | 0.0572652 | + | 0.0991862i | 0.893237 | − | 0.449586i | \(-0.148429\pi\) |
−0.835972 | + | 0.548773i | \(0.815095\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3484.00 | + | 6034.47i | −0.291290 | + | 0.504529i | −0.974115 | − | 0.226053i | \(-0.927418\pi\) |
0.682825 | + | 0.730582i | \(0.260751\pi\) | |||||||
\(524\) | 3392.00 | 0.282787 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −336.000 | −0.0278523 | ||||||||
\(527\) | 2664.00 | − | 4614.18i | 0.220200 | − | 0.381398i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −188.500 | − | 326.492i | −0.0154927 | − | 0.0268342i | ||||
\(530\) | 4452.00 | − | 7711.09i | 0.364873 | − | 0.631978i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2916.00 | −0.236972 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3108.00 | + | 5383.21i | 0.251160 | + | 0.435022i | ||||
\(536\) | 2864.00 | + | 4960.59i | 0.230795 | + | 0.399748i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2620.00 | 0.209956 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3531.00 | + | 6115.87i | −0.280609 | + | 0.486029i | −0.971535 | − | 0.236896i | \(-0.923870\pi\) |
0.690926 | + | 0.722926i | \(0.257203\pi\) | |||||||
\(542\) | 2208.00 | + | 3824.37i | 0.174985 | + | 0.303082i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1184.00 | − | 2050.75i | 0.0933154 | − | 0.161627i | ||||
\(545\) | 26180.0 | 2.05767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8196.00 | −0.640650 | −0.320325 | − | 0.947308i | \(-0.603792\pi\) | ||||
−0.320325 | + | 0.947308i | \(0.603792\pi\) | |||||||
\(548\) | −5932.00 | + | 10274.5i | −0.462413 | + | 0.800923i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1988.00 | − | 3443.32i | −0.154125 | − | 0.266952i | ||||
\(551\) | 7600.00 | − | 13163.6i | 0.587606 | − | 1.01776i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10588.0 | 0.811987 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5600.00 | − | 9699.48i | −0.427146 | − | 0.739838i | ||||
\(557\) | −3733.00 | − | 6465.75i | −0.283972 | − | 0.491854i | 0.688388 | − | 0.725343i | \(-0.258319\pi\) |
−0.972359 | + | 0.233490i | \(0.924986\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7416.00 | −0.561115 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3242.00 | − | 5615.31i | 0.243337 | − | 0.421472i | ||||
\(563\) | 12484.0 | + | 21622.9i | 0.934526 | + | 1.61865i | 0.775478 | + | 0.631375i | \(0.217509\pi\) |
0.159048 | + | 0.987271i | \(0.449158\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9646.00 | − | 16707.4i | 0.718248 | − | 1.24404i | ||||
\(566\) | −3184.00 | −0.236455 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3136.00 | −0.231661 | ||||||||
\(569\) | 7125.00 | − | 12340.9i | 0.524948 | − | 0.909237i | −0.474630 | − | 0.880186i | \(-0.657418\pi\) |
0.999578 | − | 0.0290514i | \(-0.00924865\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3186.00 | − | 5518.31i | −0.233503 | − | 0.404438i | 0.725334 | − | 0.688397i | \(-0.241685\pi\) |
−0.958836 | + | 0.283959i | \(0.908352\pi\) | |||||||
\(572\) | −1008.00 | + | 1745.91i | −0.0736829 | + | 0.127622i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7952.00 | 0.576733 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4183.00 | + | 7245.17i | 0.301803 | + | 0.522739i | 0.976545 | − | 0.215316i | \(-0.0690780\pi\) |
−0.674741 | + | 0.738055i | \(0.735745\pi\) | |||||||
\(578\) | −563.000 | − | 975.145i | −0.0405151 | − | 0.0701742i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10640.0 | −0.761728 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4452.00 | − | 7711.09i | 0.316266 | − | 0.547789i | ||||
\(584\) | −2152.00 | − | 3727.37i | −0.152484 | − | 0.264109i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5022.00 | + | 8698.36i | −0.354022 | + | 0.613184i | ||||
\(587\) | −20384.0 | −1.43328 | −0.716642 | − | 0.697441i | \(-0.754322\pi\) | ||||
−0.716642 | + | 0.697441i | \(0.754322\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5760.00 | 0.402948 | ||||||||
\(590\) | −2800.00 | + | 4849.74i | −0.195380 | + | 0.338408i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2768.00 | + | 4794.32i | 0.192169 | + | 0.332847i | ||||
\(593\) | 4689.00 | − | 8121.59i | 0.324712 | − | 0.562417i | −0.656742 | − | 0.754115i | \(-0.728066\pi\) |
0.981454 | + | 0.191698i | \(0.0613993\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2040.00 | −0.140204 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2016.00 | − | 3491.81i | −0.137860 | − | 0.238781i | ||||
\(599\) | −4500.00 | − | 7794.23i | −0.306953 | − | 0.531659i | 0.670741 | − | 0.741692i | \(-0.265976\pi\) |
−0.977694 | + | 0.210033i | \(0.932643\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7562.00 | 0.513245 | 0.256623 | − | 0.966512i | \(-0.417390\pi\) | ||||
0.256623 | + | 0.966512i | \(0.417390\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1184.00 | + | 2050.75i | −0.0797620 | + | 0.138152i | ||||
\(605\) | 3829.00 | + | 6632.02i | 0.257307 | + | 0.445670i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1488.00 | − | 2577.29i | 0.0994993 | − | 0.172338i | −0.811978 | − | 0.583688i | \(-0.801609\pi\) |
0.911478 | + | 0.411350i | \(0.134943\pi\) | |||||||
\(608\) | 2560.00 | 0.170759 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5544.00 | −0.367984 | ||||||||
\(611\) | 216.000 | − | 374.123i | 0.0143018 | − | 0.0247715i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2139.00 | − | 3704.86i | −0.140935 | − | 0.244107i | 0.786914 | − | 0.617063i | \(-0.211678\pi\) |
−0.927849 | + | 0.372956i | \(0.878344\pi\) | |||||||
\(614\) | 9536.00 | − | 16516.8i | 0.626778 | − | 1.08561i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18794.0 | −1.22629 | −0.613143 | − | 0.789972i | \(-0.710095\pi\) | ||||
−0.613143 | + | 0.789972i | \(0.710095\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9020.00 | − | 15623.1i | −0.585694 | − | 1.01445i | −0.994789 | − | 0.101959i | \(-0.967489\pi\) |
0.409095 | − | 0.912492i | \(-0.365845\pi\) | |||||||
\(620\) | −2016.00 | − | 3491.81i | −0.130588 | − | 0.226185i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1936.00 | 0.124801 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9729.50 | − | 16852.0i | 0.622688 | − | 1.07853i | ||||
\(626\) | −3058.00 | − | 5296.61i | −0.195243 | − | 0.338171i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5372.00 | − | 9304.58i | 0.341347 | − | 0.591231i | ||||
\(629\) | 25604.0 | 1.62305 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21688.0 | −1.36828 | −0.684141 | − | 0.729350i | \(-0.739823\pi\) | ||||
−0.684141 | + | 0.729350i | \(0.739823\pi\) | |||||||
\(632\) | −960.000 | + | 1662.77i | −0.0604221 | + | 0.104654i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4986.00 | − | 8636.01i | −0.312333 | − | 0.540977i | ||||
\(635\) | −13608.0 | + | 23569.7i | −0.850420 | + | 1.47297i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10640.0 | −0.660253 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −896.000 | − | 1551.92i | −0.0553399 | − | 0.0958514i | ||||
\(641\) | −5279.00 | − | 9143.50i | −0.325285 | − | 0.563411i | 0.656285 | − | 0.754513i | \(-0.272127\pi\) |
−0.981570 | + | 0.191102i | \(0.938794\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26152.0 | −1.60394 | −0.801971 | − | 0.597363i | \(-0.796215\pi\) | ||||
−0.801971 | + | 0.597363i | \(0.796215\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5920.00 | − | 10253.7i | 0.360556 | − | 0.624502i | ||||
\(647\) | 12792.0 | + | 22156.4i | 0.777288 | + | 1.34630i | 0.933499 | + | 0.358579i | \(0.116739\pi\) |
−0.156211 | + | 0.987724i | \(0.549928\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2800.00 | + | 4849.74i | −0.169352 | + | 0.293327i | ||||
\(650\) | 2556.00 | 0.154238 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4048.00 | −0.243147 | ||||||||
\(653\) | 7599.00 | − | 13161.9i | 0.455393 | − | 0.788764i | −0.543317 | − | 0.839527i | \(-0.682832\pi\) |
0.998711 | + | 0.0507630i | \(0.0161653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5936.00 | − | 10281.5i | −0.354105 | − | 0.613328i | ||||
\(656\) | 1296.00 | − | 2244.74i | 0.0771346 | − | 0.133601i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6100.00 | 0.360580 | 0.180290 | − | 0.983613i | \(-0.442296\pi\) | ||||
0.180290 | + | 0.983613i | \(0.442296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1159.00 | + | 2007.45i | 0.0681995 | + | 0.118125i | 0.898109 | − | 0.439773i | \(-0.144941\pi\) |
−0.829909 | + | 0.557898i | \(0.811608\pi\) | |||||||
\(662\) | −8612.00 | − | 14916.4i | −0.505612 | − | 0.875745i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8576.00 | 0.501225 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10640.0 | − | 18429.0i | 0.617665 | − | 1.06983i | ||||
\(668\) | 1088.00 | + | 1884.47i | 0.0630179 | + | 0.109150i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10024.0 | − | 17362.1i | 0.578001 | − | 1.00113i | ||||
\(671\) | −5544.00 | −0.318962 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10222.0 | −0.585482 | −0.292741 | − | 0.956192i | \(-0.594567\pi\) | ||||
−0.292741 | + | 0.956192i | \(0.594567\pi\) | |||||||
\(674\) | 10206.0 | − | 17677.3i | 0.583265 | − | 1.01024i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3746.00 | + | 6488.26i | 0.213132 | + | 0.369155i | ||||
\(677\) | 12717.0 | − | 22026.5i | 0.721941 | − | 1.25044i | −0.238280 | − | 0.971197i | \(-0.576584\pi\) |
0.960221 | − | 0.279242i | \(-0.0900831\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8288.00 | −0.467397 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2016.00 | − | 3491.81i | −0.113192 | − | 0.196053i | ||||
\(683\) | −4266.00 | − | 7388.93i | −0.238996 | − | 0.413952i | 0.721431 | − | 0.692487i | \(-0.243485\pi\) |
−0.960426 | + | 0.278534i | \(0.910151\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41524.0 | 2.31613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3296.00 | − | 5708.84i | 0.182644 | − | 0.316348i | ||||
\(689\) | 2862.00 | + | 4957.13i | 0.158249 | + | 0.274095i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10336.0 | + | 17902.5i | −0.569030 | + | 0.985589i | 0.427632 | + | 0.903953i | \(0.359348\pi\) |
−0.996662 | + | 0.0816365i | \(0.973985\pi\) | |||||||
\(692\) | −7432.00 | −0.408269 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4008.00 | −0.219224 | ||||||||
\(695\) | −19600.0 | + | 33948.2i | −1.06974 | + | 1.85285i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5994.00 | − | 10381.9i | −0.325737 | − | 0.564194i | ||||
\(698\) | −1330.00 | + | 2303.63i | −0.0721221 | + | 0.124919i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21458.0 | 1.15614 | 0.578072 | − | 0.815985i | \(-0.303805\pi\) | ||||
0.578072 | + | 0.815985i | \(0.303805\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13840.0 | + | 23971.6i | 0.742511 | + | 1.28607i | ||||
\(704\) | −896.000 | − | 1551.92i | −0.0479677 | − | 0.0830825i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1956.00 | −0.104271 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4925.00 | − | 8530.35i | 0.260878 | − | 0.451853i | −0.705598 | − | 0.708613i | \(-0.749321\pi\) |
0.966475 | + | 0.256759i | \(0.0826547\pi\) | |||||||
\(710\) | 5488.00 | + | 9505.49i | 0.290086 | + | 0.502443i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3240.00 | − | 5611.84i | 0.170540 | − | 0.295383i | ||||
\(713\) | 8064.00 | 0.423561 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7056.00 | 0.369062 | ||||||||
\(716\) | −600.000 | + | 1039.23i | −0.0313171 | + | 0.0542428i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9680.00 | − | 16766.3i | −0.503140 | − | 0.871464i | ||||
\(719\) | −9420.00 | + | 16315.9i | −0.488605 | + | 0.846288i | −0.999914 | − | 0.0131086i | \(-0.995827\pi\) |
0.511309 | + | 0.859397i | \(0.329161\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −918.000 | −0.0473191 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4716.00 | + | 8168.35i | 0.242084 | + | 0.419302i | ||||
\(725\) | 6745.00 | + | 11682.7i | 0.345521 | + | 0.598461i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37504.0 | 1.91327 | 0.956634 | − | 0.291291i | \(-0.0940849\pi\) | ||||
0.956634 | + | 0.291291i | \(0.0940849\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7532.00 | + | 13045.8i | −0.381879 | + | 0.661434i | ||||
\(731\) | −15244.0 | − | 26403.4i | −0.771299 | − | 1.33593i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6669.00 | + | 11551.0i | −0.336051 | + | 0.582057i | −0.983686 | − | 0.179894i | \(-0.942425\pi\) |
0.647635 | + | 0.761950i | \(0.275758\pi\) | |||||||
\(734\) | −17312.0 | −0.870569 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3584.00 | 0.179495 | ||||||||
\(737\) | 10024.0 | − | 17362.1i | 0.501002 | − | 0.867762i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8550.00 | − | 14809.0i | −0.425598 | − | 0.737157i | 0.570878 | − | 0.821035i | \(-0.306603\pi\) |
−0.996476 | + | 0.0838776i | \(0.973270\pi\) | |||||||
\(740\) | 9688.00 | − | 16780.1i | 0.481268 | − | 0.833580i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19632.0 | 0.969352 | 0.484676 | − | 0.874694i | \(-0.338938\pi\) | ||||
0.484676 | + | 0.874694i | \(0.338938\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3570.00 | + | 6183.42i | 0.175563 | + | 0.304085i | ||||
\(746\) | −5278.00 | − | 9141.76i | −0.259037 | − | 0.448665i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8288.00 | −0.405133 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16956.0 | + | 29368.7i | −0.823879 | + | 1.42700i | 0.0788938 | + | 0.996883i | \(0.474861\pi\) |
−0.902773 | + | 0.430117i | \(0.858472\pi\) | |||||||
\(752\) | 192.000 | + | 332.554i | 0.00931053 | + | 0.0161263i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3420.00 | − | 5923.61i | 0.165184 | − | 0.286108i | ||||
\(755\) | 8288.00 | 0.399512 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31386.0 | −1.50693 | −0.753463 | − | 0.657490i | \(-0.771618\pi\) | ||||
−0.753463 | + | 0.657490i | \(0.771618\pi\) | |||||||
\(758\) | −6340.00 | + | 10981.2i | −0.303798 | + | 0.526194i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4480.00 | − | 7759.59i | −0.213825 | − | 0.370355i | ||||
\(761\) | −17279.0 | + | 29928.1i | −0.823079 | + | 1.42561i | 0.0802993 | + | 0.996771i | \(0.474412\pi\) |
−0.903378 | + | 0.428844i | \(0.858921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5568.00 | −0.263669 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6232.00 | − | 10794.1i | −0.293957 | − | 0.509149i | ||||
\(767\) | −1800.00 | − | 3117.69i | −0.0847382 | − | 0.146771i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39130.0 | 1.83493 | 0.917467 | − | 0.397812i | \(-0.130231\pi\) | ||||
0.917467 | + | 0.397812i | \(0.130231\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3556.00 | + | 6159.17i | −0.165781 | + | 0.287142i | ||||
\(773\) | −12991.0 | − | 22501.1i | −0.604468 | − | 1.04697i | −0.992135 | − | 0.125170i | \(-0.960052\pi\) |
0.387667 | − | 0.921799i | \(-0.373281\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2556.00 | + | 4427.12i | −0.118470 | + | 0.205196i | ||||
\(776\) | 10832.0 | 0.501090 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 29620.0 | 1.36495 | ||||||||
\(779\) | 6480.00 | − | 11223.7i | 0.298036 | − | 0.516214i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5488.00 | + | 9505.49i | 0.251442 | + | 0.435510i | ||||
\(782\) | 8288.00 | − | 14355.2i | 0.379000 | − | 0.656448i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37604.0 | −1.70974 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17712.0 | − | 30678.1i | −0.802242 | − | 1.38952i | −0.918137 | − | 0.396263i | \(-0.870307\pi\) |
0.115895 | − | 0.993261i | \(-0.463026\pi\) | |||||||
\(788\) | 2428.00 | + | 4205.42i | 0.109764 | + | 0.190117i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6720.00 | 0.302642 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1782.00 | − | 3086.51i | 0.0797991 | − | 0.138216i | ||||
\(794\) | −5154.00 | − | 8926.99i | −0.230363 | − | 0.399001i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2080.00 | + | 3602.67i | −0.0926176 | + | 0.160418i | ||||
\(797\) | 30606.0 | 1.36025 | 0.680126 | − | 0.733096i | \(-0.261925\pi\) | ||||
0.680126 | + | 0.733096i | \(0.261925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1776.00 | 0.0786362 | ||||||||
\(800\) | −1136.00 | + | 1967.61i | −0.0502046 | + | 0.0869569i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3282.00 | + | 5684.59i | 0.144503 | + | 0.250287i | ||||
\(803\) | −7532.00 | + | 13045.8i | −0.331007 | + | 0.573321i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2592.00 | 0.113275 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5432.00 | − | 9408.50i | −0.236506 | − | 0.409641i | ||||
\(809\) | 8405.00 | + | 14557.9i | 0.365271 | + | 0.632668i | 0.988820 | − | 0.149117i | \(-0.0476431\pi\) |
−0.623549 | + | 0.781784i | \(0.714310\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9368.00 | −0.405616 | −0.202808 | − | 0.979218i | \(-0.565007\pi\) | ||||
−0.202808 | + | 0.979218i | \(0.565007\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9688.00 | − | 16780.1i | 0.417155 | − | 0.722534i | ||||
\(815\) | 7084.00 | + | 12269.8i | 0.304468 | + | 0.527355i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16480.0 | − | 28544.2i | 0.705707 | − | 1.22232i | ||||
\(818\) | 11620.0 | 0.496679 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9072.00 | −0.386351 | ||||||||
\(821\) | 17191.0 | − | 29775.7i | 0.730780 | − | 1.26575i | −0.225771 | − | 0.974180i | \(-0.572490\pi\) |
0.956550 | − | 0.291567i | \(-0.0941766\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2236.00 | + | 3872.87i | 0.0947048 | + | 0.164034i | 0.909485 | − | 0.415736i | \(-0.136476\pi\) |
−0.814781 | + | 0.579769i | \(0.803143\pi\) | |||||||
\(824\) | 3328.00 | − | 5764.27i | 0.140699 | − | 0.243699i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1716.00 | 0.0721538 | 0.0360769 | − | 0.999349i | \(-0.488514\pi\) | ||||
0.0360769 | + | 0.999349i | \(0.488514\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3955.00 | + | 6850.26i | 0.165697 | + | 0.286996i | 0.936903 | − | 0.349591i | \(-0.113679\pi\) |
−0.771206 | + | 0.636586i | \(0.780346\pi\) | |||||||
\(830\) | −15008.0 | − | 25994.6i | −0.627633 | − | 1.08709i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1152.00 | 0.0480029 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3808.00 | − | 6595.65i | 0.157822 | − | 0.273356i | ||||
\(836\) | −4480.00 | − | 7759.59i | −0.185340 | − | 0.321018i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13560.0 | − | 23486.6i | 0.558977 | − | 0.968176i | ||||
\(839\) | 19360.0 | 0.796641 | 0.398320 | − | 0.917246i | \(-0.369593\pi\) | ||||
0.398320 | + | 0.917246i | \(0.369593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11711.0 | 0.480175 | ||||||||
\(842\) | 738.000 | − | 1278.25i | 0.0302057 | − | 0.0523177i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7736.00 | + | 13399.1i | 0.315502 | + | 0.546466i | ||||
\(845\) | 13111.0 | − | 22708.9i | 0.533766 | − | 0.924510i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5088.00 | −0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5254.00 | + | 9100.19i | 0.212013 | + | 0.367217i | ||||
\(851\) | 19376.0 | + | 33560.2i | 0.780494 | + | 1.35186i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 698.000 | 0.0280177 | 0.0140088 | − | 0.999902i | \(-0.495541\pi\) | ||||
0.0140088 | + | 0.999902i | \(0.495541\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1776.00 | − | 3076.12i | 0.0709141 | − | 0.122827i | ||||
\(857\) | −11703.0 | − | 20270.2i | −0.466472 | − | 0.807954i | 0.532794 | − | 0.846245i | \(-0.321142\pi\) |
−0.999267 | + | 0.0382909i | \(0.987809\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3640.00 | + | 6304.66i | −0.144581 | + | 0.250422i | −0.929217 | − | 0.369536i | \(-0.879517\pi\) |
0.784635 | + | 0.619957i | \(0.212850\pi\) | |||||||
\(860\) | −23072.0 | −0.914824 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2544.00 | −0.100521 | ||||||||
\(863\) | 4904.00 | − | 8493.98i | 0.193435 | − | 0.335039i | −0.752952 | − | 0.658076i | \(-0.771371\pi\) |
0.946386 | + | 0.323037i | \(0.104704\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13006.0 | + | 22527.1i | 0.511234 | + | 0.885483i | ||||
\(866\) | 5062.00 | − | 8767.64i | 0.198630 | − | 0.344038i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6720.00 | 0.262325 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6444.00 | + | 11161.3i | 0.250685 | + | 0.434199i | ||||
\(872\) | −7480.00 | − | 12955.7i | −0.290487 | − | 0.503138i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17920.0 | 0.693539 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4033.00 | − | 6985.36i | 0.155285 | − | 0.268961i | −0.777878 | − | 0.628415i | \(-0.783704\pi\) |
0.933163 | + | 0.359454i | \(0.117037\pi\) | |||||||
\(878\) | −5640.00 | − | 9768.77i | −0.216789 | − | 0.375490i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3136.00 | + | 5431.71i | −0.120130 | + | 0.208072i | ||||
\(881\) | −25842.0 | −0.988240 | −0.494120 | − | 0.869394i | \(-0.664510\pi\) | ||||
−0.494120 | + | 0.869394i | \(0.664510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5692.00 | −0.216932 | −0.108466 | − | 0.994100i | \(-0.534594\pi\) | ||||
−0.108466 | + | 0.994100i | \(0.534594\pi\) | |||||||
\(884\) | 2664.00 | − | 4614.18i | 0.101357 | − | 0.175556i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13388.0 | + | 23188.7i | 0.507651 | + | 0.879277i | ||||
\(887\) | −6768.00 | + | 11722.5i | −0.256198 | + | 0.443747i | −0.965220 | − | 0.261439i | \(-0.915803\pi\) |
0.709023 | + | 0.705186i | \(0.249136\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −22680.0 | −0.854197 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7936.00 | − | 13745.6i | −0.297889 | − | 0.515959i | ||||
\(893\) | 960.000 | + | 1662.77i | 0.0359744 | + | 0.0623096i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4200.00 | 0.156861 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3230.00 | + | 5594.52i | −0.120030 | + | 0.207897i | ||||
\(899\) | 6840.00 | + | 11847.2i | 0.253756 | + | 0.439519i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11766.0 | + | 20379.3i | −0.435052 | + | 0.753533i | ||||
\(902\) | −9072.00 | −0.334883 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11024.0 | −0.405589 | ||||||||
\(905\) | 16506.0 | − | 28589.2i | 0.606274 | − | 1.05010i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8502.00 | − | 14725.9i | −0.311251 | − | 0.539102i | 0.667383 | − | 0.744715i | \(-0.267415\pi\) |
−0.978633 | + | 0.205613i | \(0.934081\pi\) | |||||||
\(908\) | −7872.00 | + | 13634.7i | −0.287711 | + | 0.498330i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14568.0 | 0.529813 | 0.264906 | − | 0.964274i | \(-0.414659\pi\) | ||||
0.264906 | + | 0.964274i | \(0.414659\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15008.0 | − | 25994.6i | −0.544022 | − | 0.942274i | ||||
\(914\) | 10646.0 | + | 18439.4i | 0.385272 | + | 0.667310i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19240.0 | 0.694004 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 700.000 | − | 1212.44i | 0.0251261 | − | 0.0435197i | −0.853189 | − | 0.521602i | \(-0.825335\pi\) |
0.878315 | + | 0.478082i | \(0.158668\pi\) | |||||||
\(920\) | −6272.00 | − | 10863.4i | −0.224763 | − | 0.389300i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7282.00 | − | 12612.8i | 0.260108 | − | 0.450521i | ||||
\(923\) | −7056.00 | −0.251626 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24566.0 | −0.873216 | ||||||||
\(926\) | −12688.0 | + | 21976.3i | −0.450274 | + | 0.779897i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3040.00 | + | 5265.43i | 0.107535 | + | 0.186257i | ||||
\(929\) | −6915.00 | + | 11977.1i | −0.244213 | + | 0.422989i | −0.961910 | − | 0.273366i | \(-0.911863\pi\) |
0.717697 | + | 0.696355i | \(0.245196\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8728.00 | 0.306754 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2816.00 | − | 4877.46i | −0.0986535 | − | 0.170873i | ||||
\(935\) | 14504.0 | + | 25121.7i | 0.507306 | + | 0.878681i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24166.0 | −0.842549 | −0.421275 | − | 0.906933i | \(-0.638417\pi\) | ||||
−0.421275 | + | 0.906933i | \(0.638417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 672.000 | − | 1163.94i | 0.0233173 | − | 0.0403867i | ||||
\(941\) | −5419.00 | − | 9385.98i | −0.187730 | − | 0.325159i | 0.756763 | − | 0.653690i | \(-0.226780\pi\) |
−0.944493 | + | 0.328531i | \(0.893446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9072.00 | − | 15713.2i | 0.313282 | − | 0.542620i | ||||
\(944\) | 3200.00 | 0.110330 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23072.0 | −0.792955 | ||||||||
\(947\) | −20458.0 | + | 35434.3i | −0.702002 | + | 1.21590i | 0.265761 | + | 0.964039i | \(0.414377\pi\) |
−0.967763 | + | 0.251864i | \(0.918957\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4842.00 | − | 8386.59i | −0.165625 | − | 0.286871i | ||||
\(950\) | −5680.00 | + | 9838.05i | −0.193983 | + | 0.335988i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56618.0 | −1.92449 | −0.962244 | − | 0.272189i | \(-0.912253\pi\) | ||||
−0.962244 | + | 0.272189i | \(0.912253\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9744.00 | + | 16877.1i | 0.330166 | + | 0.571864i | ||||
\(956\) | −6000.00 | − | 10392.3i | −0.202985 | − | 0.351581i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6320.00 | 0.213142 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12303.5 | − | 21310.3i | 0.412994 | − | 0.715326i | ||||
\(962\) | 6228.00 | + | 10787.2i | 0.208731 | + | 0.361532i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4084.00 | + | 7073.70i | −0.136449 | + | 0.236337i | ||||
\(965\) | 24892.0 | 0.830365 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17504.0 | 0.582100 | 0.291050 | − | 0.956708i | \(-0.405995\pi\) | ||||
0.291050 | + | 0.956708i | \(0.405995\pi\) | |||||||
\(968\) | 2188.00 | − | 3789.73i | 0.0726498 | − | 0.125833i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18956.0 | − | 32832.8i | −0.627464 | − | 1.08680i | ||||
\(971\) | 11556.0 | − | 20015.6i | 0.381926 | − | 0.661514i | −0.609412 | − | 0.792854i | \(-0.708594\pi\) |
0.991337 | + | 0.131339i | \(0.0419277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −28352.0 | −0.932707 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1584.00 | + | 2743.57i | 0.0519494 | + | 0.0899790i | ||||
\(977\) | 11937.0 | + | 20675.5i | 0.390889 | + | 0.677039i | 0.992567 | − | 0.121699i | \(-0.0388343\pi\) |
−0.601678 | + | 0.798739i | \(0.705501\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22680.0 | −0.740404 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11268.0 | + | 19516.7i | −0.366167 | + | 0.634220i | ||||
\(983\) | −7656.00 | − | 13260.6i | −0.248411 | − | 0.430261i | 0.714674 | − | 0.699458i | \(-0.246575\pi\) |
−0.963085 | + | 0.269197i | \(0.913242\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8498.00 | − | 14719.0i | 0.274892 | − | 0.476127i | ||||
\(986\) | 28120.0 | 0.908239 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5760.00 | 0.185476 | ||||||||
\(989\) | 23072.0 | − | 39961.9i | 0.741807 | − | 1.28485i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8264.00 | + | 14313.7i | 0.264899 | + | 0.458818i | 0.967537 | − | 0.252729i | \(-0.0813281\pi\) |
−0.702638 | + | 0.711547i | \(0.747995\pi\) | |||||||
\(992\) | −1152.00 | + | 1995.32i | −0.0368710 | + | 0.0638625i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14560.0 | 0.463903 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14303.0 | + | 24773.5i | 0.454344 | + | 0.786946i | 0.998650 | − | 0.0519402i | \(-0.0165405\pi\) |
−0.544307 | + | 0.838886i | \(0.683207\pi\) | |||||||
\(998\) | 4460.00 | + | 7724.95i | 0.141462 | + | 0.245019i | ||||
\(999\) | 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 | 882.4.g.b.667.1 | 2 | ||
3.2 | odd | 2 | 98.4.c.d.79.1 | 2 | |||
7.2 | even | 3 | 126.4.a.h.1.1 | 1 | |||
7.3 | odd | 6 | 882.4.g.k.361.1 | 2 | |||
7.4 | even | 3 | inner | 882.4.g.b.361.1 | 2 | ||
7.5 | odd | 6 | 882.4.a.i.1.1 | 1 | |||
7.6 | odd | 2 | 882.4.g.k.667.1 | 2 | |||
21.2 | odd | 6 | 14.4.a.a.1.1 | ✓ | 1 | ||
21.5 | even | 6 | 98.4.a.a.1.1 | 1 | |||
21.11 | odd | 6 | 98.4.c.d.67.1 | 2 | |||
21.17 | even | 6 | 98.4.c.f.67.1 | 2 | |||
21.20 | even | 2 | 98.4.c.f.79.1 | 2 | |||
28.23 | odd | 6 | 1008.4.a.s.1.1 | 1 | |||
84.23 | even | 6 | 112.4.a.a.1.1 | 1 | |||
84.47 | odd | 6 | 784.4.a.s.1.1 | 1 | |||
105.2 | even | 12 | 350.4.c.b.99.1 | 2 | |||
105.23 | even | 12 | 350.4.c.b.99.2 | 2 | |||
105.44 | odd | 6 | 350.4.a.l.1.1 | 1 | |||
105.89 | even | 6 | 2450.4.a.bo.1.1 | 1 | |||
168.107 | even | 6 | 448.4.a.o.1.1 | 1 | |||
168.149 | odd | 6 | 448.4.a.b.1.1 | 1 | |||
231.65 | even | 6 | 1694.4.a.g.1.1 | 1 | |||
273.233 | odd | 6 | 2366.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.4.a.a.1.1 | ✓ | 1 | 21.2 | odd | 6 | ||
98.4.a.a.1.1 | 1 | 21.5 | even | 6 | |||
98.4.c.d.67.1 | 2 | 21.11 | odd | 6 | |||
98.4.c.d.79.1 | 2 | 3.2 | odd | 2 | |||
98.4.c.f.67.1 | 2 | 21.17 | even | 6 | |||
98.4.c.f.79.1 | 2 | 21.20 | even | 2 | |||
112.4.a.a.1.1 | 1 | 84.23 | even | 6 | |||
126.4.a.h.1.1 | 1 | 7.2 | even | 3 | |||
350.4.a.l.1.1 | 1 | 105.44 | odd | 6 | |||
350.4.c.b.99.1 | 2 | 105.2 | even | 12 | |||
350.4.c.b.99.2 | 2 | 105.23 | even | 12 | |||
448.4.a.b.1.1 | 1 | 168.149 | odd | 6 | |||
448.4.a.o.1.1 | 1 | 168.107 | even | 6 | |||
784.4.a.s.1.1 | 1 | 84.47 | odd | 6 | |||
882.4.a.i.1.1 | 1 | 7.5 | odd | 6 | |||
882.4.g.b.361.1 | 2 | 7.4 | even | 3 | inner | ||
882.4.g.b.667.1 | 2 | 1.1 | even | 1 | trivial | ||
882.4.g.k.361.1 | 2 | 7.3 | odd | 6 | |||
882.4.g.k.667.1 | 2 | 7.6 | odd | 2 | |||
1008.4.a.s.1.1 | 1 | 28.23 | odd | 6 | |||
1694.4.a.g.1.1 | 1 | 231.65 | even | 6 | |||
2366.4.a.h.1.1 | 1 | 273.233 | odd | 6 | |||
2450.4.a.bo.1.1 | 1 | 105.89 | even | 6 |