Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 24.2982565319 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.785053338\) \(a_{3}=-0.577350269\) \(a_{4}=+2.186415419\) \(a_{5}=-1.254281202\)
\(a_{6}=+1.030601025\) \(a_{7}=+0.788847251\) \(a_{8}=-2.117814803\) \(a_{9}=+0.333333333\) \(a_{10}=+2.238958846\)
\(a_{11}=+1.328357482\) \(a_{12}=-1.262327531\) \(a_{13}=+1.215850884\) \(a_{14}=-1.408134418\) \(a_{15}=+0.724159589\)
\(a_{16}=+1.593996965\) \(a_{17}=-0.971874191\) \(a_{18}=-0.595017779\) \(a_{19}=-0.136251035\) \(a_{20}=-2.742379759\)
\(a_{21}=-0.455441173\) \(a_{22}=-2.371188957\) \(a_{23}=-0.184277377\) \(a_{24}=+1.222720947\) \(a_{25}=+0.573221333\)
\(a_{26}=-2.170358679\) \(a_{27}=-0.192450090\) \(a_{28}=+1.724747792\) \(a_{29}=-1.145003281\) \(a_{30}=-1.292663492\)
\(a_{31}=-0.007409006\) \(a_{32}=-0.727554799\) \(a_{33}=-0.766927550\) \(a_{34}=+1.734847269\) \(a_{35}=-0.989436278\)
\(a_{36}=+0.728805140\) \(a_{37}=+1.193073567\) \(a_{38}=+0.243215365\) \(a_{39}=-0.701971835\) \(a_{40}=+2.656335297\)
\(a_{41}=-0.097556604\) \(a_{42}=+0.812986785\) \(a_{43}=-1.171114262\) \(a_{44}=+2.904341281\) \(a_{45}=-0.418093734\)
\(a_{46}=+0.328944947\) \(a_{47}=+1.541151233\) \(a_{48}=-0.920294577\) \(a_{49}=-0.377720015\) \(a_{50}=-1.023230654\)
\(a_{51}=+0.561111826\) \(a_{52}=+2.658355120\) \(a_{53}=+0.503182262\) \(a_{54}=+0.343533675\) \(a_{55}=-1.666133819\)
\(a_{56}=-1.670632385\) \(a_{57}=+0.078664572\) \(a_{58}=+2.043891929\) \(a_{59}=-1.546287864\) \(a_{60}=+1.583313692\)
\(a_{61}=+0.138404930\) \(a_{62}=+0.013225471\) \(a_{63}=+0.262949084\) \(a_{64}=-0.295272842\) \(a_{65}=-1.525018908\)
\(a_{66}=+1.369006583\) \(a_{67}=+0.079271581\) \(a_{68}=-2.124920717\) \(a_{69}=+0.106392593\) \(a_{70}=+1.766196530\)
\(a_{71}=+1.152846516\) \(a_{72}=-0.705938268\) \(a_{73}=+0.974924428\) \(a_{74}=-2.129699953\) \(a_{75}=-0.330949491\)
\(a_{76}=-0.297901364\) \(a_{77}=+1.047871148\) \(a_{78}=+1.253057168\) \(a_{79}=+0.241352452\) \(a_{80}=-1.999320429\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.174143742\) \(a_{83}=-0.301912861\) \(a_{84}=-0.995783602\) \(a_{85}=+1.219003529\)
\(a_{86}=+2.090501422\) \(a_{87}=+0.661067953\) \(a_{88}=-2.813215140\) \(a_{89}=-0.194295048\) \(a_{90}=+0.746319615\)
\(a_{91}=+0.959120627\) \(a_{92}=-0.402906898\) \(a_{93}=+0.004277592\) \(a_{94}=-2.751037152\) \(a_{95}=+0.170897112\)
\(a_{96}=+0.420053959\) \(a_{97}=+1.048700239\) \(a_{98}=+0.674250373\) \(a_{99}=+0.442785827\) \(a_{100}=+1.253299961\)

Showing 100 of 1228 available coefficients

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