Properties

Level $21$
Weight $0$
Character 21.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 6.56709384047 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.284442408\) \(a_{3}=+0.577350269\) \(a_{4}=-0.919092517\) \(a_{5}=+1.900334858\)
\(a_{6}=+0.164222901\) \(a_{7}=-0.377964473\) \(a_{8}=-0.545871296\) \(a_{9}=+0.333333333\) \(a_{10}=+0.540535823\)
\(a_{11}=-0.617139987\) \(a_{12}=-0.530638312\) \(a_{13}=+1.187083363\) \(a_{14}=-0.107509125\) \(a_{15}=+1.097158842\)
\(a_{16}=+0.763823571\) \(a_{17}=+0.912077468\) \(a_{18}=+0.094814136\) \(a_{19}=+0.838199179\) \(a_{20}=-1.746583547\)
\(a_{21}=-0.218217890\) \(a_{22}=-0.175540784\) \(a_{23}=+1.021436373\) \(a_{24}=-0.315158940\) \(a_{25}=+2.611272573\)
\(a_{26}=+0.337656850\) \(a_{27}=+0.192450090\) \(a_{28}=+0.347384319\) \(a_{29}=-0.468525244\) \(a_{30}=+0.312078503\)
\(a_{31}=-0.853126124\) \(a_{32}=+0.763135112\) \(a_{33}=-0.356305938\) \(a_{34}=+0.259433511\) \(a_{35}=-0.718259063\)
\(a_{36}=-0.306364172\) \(a_{37}=+0.964720369\) \(a_{38}=+0.238419393\) \(a_{39}=+0.685362899\) \(a_{40}=-1.037338253\)
\(a_{41}=-1.015266912\) \(a_{42}=-0.062070422\) \(a_{43}=-0.553191405\) \(a_{44}=+0.567208744\) \(a_{45}=+0.633444953\)
\(a_{46}=+0.290539821\) \(a_{47}=-0.230631759\) \(a_{48}=+0.440993744\) \(a_{49}=+0.142857143\) \(a_{50}=+0.742756658\)
\(a_{51}=+0.526588171\) \(a_{52}=-1.091039435\) \(a_{53}=+0.973704205\) \(a_{54}=+0.054740967\) \(a_{55}=-1.172772630\)
\(a_{56}=+0.206319957\) \(a_{57}=+0.483934521\) \(a_{58}=-0.133268448\) \(a_{59}=-0.008887830\) \(a_{60}=-1.008390481\)
\(a_{61}=+0.733701731\) \(a_{62}=-0.242665249\) \(a_{63}=-0.125988158\) \(a_{64}=-0.546755582\) \(a_{65}=+2.255855894\)
\(a_{66}=-0.101348519\) \(a_{67}=-1.684398315\) \(a_{68}=-0.838283575\) \(a_{69}=+0.589726565\) \(a_{70}=-0.204303337\)
\(a_{71}=-1.346659133\) \(a_{72}=-0.181957099\) \(a_{73}=-0.351063699\) \(a_{74}=+0.274407385\) \(a_{75}=+1.507618923\)
\(a_{76}=-0.770382592\) \(a_{77}=+0.233256990\) \(a_{78}=+0.194946273\) \(a_{79}=+0.286051797\) \(a_{80}=+1.451520557\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.288784965\) \(a_{83}=-0.134193444\) \(a_{84}=+0.200562430\) \(a_{85}=+1.733252605\)
\(a_{86}=-0.157351095\) \(a_{87}=-0.270503176\) \(a_{88}=+0.336879005\) \(a_{89}=-1.417947506\) \(a_{90}=+0.180178608\)
\(a_{91}=-0.448675338\) \(a_{92}=-0.938794527\) \(a_{93}=-0.492552597\) \(a_{94}=-0.065601453\) \(a_{95}=+1.592859117\)
\(a_{96}=+0.440596262\) \(a_{97}=+1.213714630\) \(a_{98}=+0.040634630\) \(a_{99}=-0.205713329\) \(a_{100}=-2.400001081\)

Showing 100 of 240 available coefficients

Rows: Cols: