Properties

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

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 19.566910611 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.565407594\) \(a_{3}=-0.577350269\) \(a_{4}=+1.450500936\) \(a_{5}=+0.622634228\)
\(a_{6}=-0.903788496\) \(a_{7}=-1.934803985\) \(a_{8}=+0.705217587\) \(a_{9}=+0.333333333\) \(a_{10}=+0.974676350\)
\(a_{11}=-0.557779987\) \(a_{12}=-0.837447106\) \(a_{13}=+0.107032892\) \(a_{14}=-3.028756851\) \(a_{15}=-0.359478039\)
\(a_{16}=-0.346547970\) \(a_{17}=+0.363486092\) \(a_{18}=+0.521802531\) \(a_{19}=-0.799142115\) \(a_{20}=+0.903131531\)
\(a_{21}=+1.117059601\) \(a_{22}=-0.873153028\) \(a_{23}=-1.659860296\) \(a_{24}=-0.407157564\) \(a_{25}=-0.612326618\)
\(a_{26}=+0.167550103\) \(a_{27}=-0.192450090\) \(a_{28}=-2.806434991\) \(a_{29}=+0.756513175\) \(a_{30}=-0.562729653\)
\(a_{31}=+0.198585301\) \(a_{32}=-1.247706411\) \(a_{33}=+0.322034426\) \(a_{34}=+0.569003889\) \(a_{35}=-1.204675186\)
\(a_{36}=+0.483500312\) \(a_{37}=+0.522725157\) \(a_{38}=-1.250983136\) \(a_{39}=-0.061795469\) \(a_{40}=+0.439092608\)
\(a_{41}=-1.199498482\) \(a_{42}=+1.748653583\) \(a_{43}=+0.936405805\) \(a_{44}=-0.809060394\) \(a_{45}=+0.207544743\)
\(a_{46}=-2.598357913\) \(a_{47}=+0.229293487\) \(a_{48}=+0.200079564\) \(a_{49}=+2.743466460\) \(a_{50}=-0.958540737\)
\(a_{51}=-0.209858793\) \(a_{52}=+0.155251311\) \(a_{53}=+0.060210170\) \(a_{54}=-0.301262832\) \(a_{55}=-0.347292912\)
\(a_{56}=-1.364457797\) \(a_{57}=+0.461384915\) \(a_{58}=+1.184251469\) \(a_{59}=+0.098773010\) \(a_{60}=-0.521423233\)
\(a_{61}=+1.234920727\) \(a_{62}=+0.310866938\) \(a_{63}=-0.644934662\) \(a_{64}=-1.606621121\) \(a_{65}=+0.066642342\)
\(a_{66}=+0.504115136\) \(a_{67}=+0.267856229\) \(a_{68}=+0.527236917\) \(a_{69}=+0.958320789\) \(a_{70}=-1.885807685\)
\(a_{71}=-0.708173333\) \(a_{72}=+0.235072529\) \(a_{73}=+0.926299540\) \(a_{74}=+0.818277931\) \(a_{75}=+0.353526937\)
\(a_{76}=-1.159156386\) \(a_{77}=+1.079194942\) \(a_{78}=-0.096735097\) \(a_{79}=-1.078127713\) \(a_{80}=-0.215772628\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.877704034\) \(a_{83}=+0.316869410\) \(a_{84}=+1.620295998\) \(a_{85}=+0.226318882\)
\(a_{86}=+1.465856758\) \(a_{87}=-0.436773085\) \(a_{88}=-0.393356257\) \(a_{89}=+0.323531806\) \(a_{90}=+0.324892117\)
\(a_{91}=-0.207087667\) \(a_{92}=-2.407628913\) \(a_{93}=-0.114653277\) \(a_{94}=+0.358937766\) \(a_{95}=-0.497573234\)
\(a_{96}=+0.720363632\) \(a_{97}=-1.250903008\) \(a_{98}=+4.294643231\) \(a_{99}=-0.185926662\) \(a_{100}=-0.888180332\)

Showing 100 of 1228 available coefficients

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