Properties

Level $21$
Weight $0$
Character 21.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 4.23037869062 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.243951116\) \(a_{3}=-0.577350269\) \(a_{4}=+0.547414378\) \(a_{5}=-1.503783940\)
\(a_{6}=+0.718195512\) \(a_{7}=-0.377964473\) \(a_{8}=+0.562994389\) \(a_{9}=+0.333333333\) \(a_{10}=+1.870633710\)
\(a_{11}=-1.102354919\) \(a_{12}=-0.316049839\) \(a_{13}=+1.150273784\) \(a_{14}=+0.470169328\) \(a_{15}=+0.868210063\)
\(a_{16}=-1.247751877\) \(a_{17}=-1.223721263\) \(a_{18}=-0.414650372\) \(a_{19}=+1.057301005\) \(a_{20}=-0.823192951\)
\(a_{21}=+0.218217890\) \(a_{22}=+1.371275631\) \(a_{23}=+0.213208303\) \(a_{24}=-0.325044962\) \(a_{25}=+1.261366139\)
\(a_{26}=-1.430884357\) \(a_{27}=-0.192450090\) \(a_{28}=-0.206903187\) \(a_{29}=+0.013098800\) \(a_{30}=-1.080010876\)
\(a_{31}=+0.364668774\) \(a_{32}=+0.989147950\) \(a_{33}=+0.636444909\) \(a_{34}=+1.522249430\) \(a_{35}=+0.568376905\)
\(a_{36}=+0.182471459\) \(a_{37}=-1.571066137\) \(a_{38}=-1.315230765\) \(a_{39}=-0.664110879\) \(a_{40}=-0.846621921\)
\(a_{41}=+1.374568079\) \(a_{42}=-0.271452388\) \(a_{43}=+0.360721418\) \(a_{44}=-0.603444933\) \(a_{45}=-0.501261313\)
\(a_{46}=-0.265220706\) \(a_{47}=-0.250757007\) \(a_{48}=+0.720389882\) \(a_{49}=+0.142857143\) \(a_{50}=-1.569077816\)
\(a_{51}=+0.706515801\) \(a_{52}=+0.629676408\) \(a_{53}=+1.225940212\) \(a_{54}=+0.239398504\) \(a_{55}=+1.657703624\)
\(a_{56}=-0.212791878\) \(a_{57}=-0.610433020\) \(a_{58}=-0.016294267\) \(a_{59}=+0.758824124\) \(a_{60}=+0.475270672\)
\(a_{61}=+0.486349451\) \(a_{62}=-0.453630128\) \(a_{63}=-0.125988158\) \(a_{64}=+0.017300181\) \(a_{65}=-1.729763244\)
\(a_{66}=-0.791706355\) \(a_{67}=+0.314375259\) \(a_{68}=-0.669882614\) \(a_{69}=-0.123095871\) \(a_{70}=-0.707033085\)
\(a_{71}=-0.983783578\) \(a_{72}=+0.187664796\) \(a_{73}=-1.441945411\) \(a_{74}=+1.954329474\) \(a_{75}=-0.728250080\)
\(a_{76}=+0.578781772\) \(a_{77}=+0.416650996\) \(a_{78}=+0.826121469\) \(a_{79}=-0.530770656\) \(a_{80}=+1.876349234\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.709895496\) \(a_{83}=-0.369181195\) \(a_{84}=+0.119455611\) \(a_{85}=+1.840212383\)
\(a_{86}=-0.448719810\) \(a_{87}=-0.007562596\) \(a_{88}=-0.620619634\) \(a_{89}=+1.812553520\) \(a_{90}=+0.623544570\)
\(a_{91}=-0.434762625\) \(a_{92}=+0.116713290\) \(a_{93}=-0.210541615\) \(a_{94}=+0.311929459\) \(a_{95}=-1.589952271\)
\(a_{96}=-0.571084835\) \(a_{97}=+0.637401903\) \(a_{98}=-0.177707302\) \(a_{99}=-0.367451640\) \(a_{100}=+0.690489961\)

Showing 100 of 232 available coefficients

Rows: Cols: