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: \( 13.1351445113 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.107752924\) \(a_{3}=-0.577350269\) \(a_{4}=-0.988389307\) \(a_{5}=+0.289837177\)
\(a_{6}=+0.062211180\) \(a_{7}=-1.240487290\) \(a_{8}=+0.214254762\) \(a_{9}=+0.333333333\) \(a_{10}=-0.031230803\)
\(a_{11}=+1.652353893\) \(a_{12}=+0.570646832\) \(a_{13}=+0.620801283\) \(a_{14}=+0.133666123\) \(a_{15}=-0.167337540\)
\(a_{16}=+0.965302663\) \(a_{17}=+0.266677701\) \(a_{18}=-0.035917641\) \(a_{19}=-0.557885376\) \(a_{20}=-0.286471967\)
\(a_{21}=+0.716195671\) \(a_{22}=-0.178045963\) \(a_{23}=+0.771745067\) \(a_{24}=-0.123700044\) \(a_{25}=-0.915994411\)
\(a_{26}=-0.066893153\) \(a_{27}=-0.192450090\) \(a_{28}=+1.226084373\) \(a_{29}=-0.813531756\) \(a_{30}=+0.018031113\)
\(a_{31}=+1.153012160\) \(a_{32}=-0.318268954\) \(a_{33}=-0.953986965\) \(a_{34}=-0.028735527\) \(a_{35}=-0.359539334\)
\(a_{36}=-0.329463102\) \(a_{37}=+1.696244124\) \(a_{38}=+0.060113781\) \(a_{39}=-0.358419787\) \(a_{40}=+0.062098995\)
\(a_{41}=-0.509873849\) \(a_{42}=-0.077172178\) \(a_{43}=+0.853630325\) \(a_{44}=-1.633168920\) \(a_{45}=+0.096612392\)
\(a_{46}=-0.083157788\) \(a_{47}=+1.670963958\) \(a_{48}=-0.557317791\) \(a_{49}=+0.538808716\) \(a_{50}=+0.098701077\)
\(a_{51}=-0.153967650\) \(a_{52}=-0.613593349\) \(a_{53}=-0.800387847\) \(a_{54}=+0.020737062\) \(a_{55}=+0.478913589\)
\(a_{56}=-0.265780314\) \(a_{57}=+0.322095268\) \(a_{58}=+0.087660433\) \(a_{59}=+0.185910451\) \(a_{60}=+0.165394655\)
\(a_{61}=+0.785568932\) \(a_{62}=-0.124240418\) \(a_{63}=-0.413495692\) \(a_{64}=-0.931008320\) \(a_{65}=+0.179931291\)
\(a_{66}=+0.102794885\) \(a_{67}=-0.146568601\) \(a_{68}=-0.263583455\) \(a_{69}=-0.445567222\) \(a_{70}=+0.038741415\)
\(a_{71}=+1.351292640\) \(a_{72}=+0.071418254\) \(a_{73}=+0.265809582\) \(a_{74}=-0.182775264\) \(a_{75}=+0.528849620\)
\(a_{76}=+0.551407940\) \(a_{77}=-2.049724002\) \(a_{78}=+0.038620780\) \(a_{79}=-0.566673638\) \(a_{80}=+0.279780618\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.054940398\) \(a_{83}=+0.849509866\) \(a_{84}=-0.707880144\) \(a_{85}=+0.077293719\)
\(a_{86}=-0.091981163\) \(a_{87}=+0.469692779\) \(a_{88}=+0.354024688\) \(a_{89}=+1.181582725\) \(a_{90}=-0.010410265\)
\(a_{91}=-0.770096097\) \(a_{92}=-0.762784573\) \(a_{93}=-0.665691888\) \(a_{94}=-0.180051248\) \(a_{95}=-0.161695915\)
\(a_{96}=+0.183752669\) \(a_{97}=+0.008194926\) \(a_{98}=-0.058058236\) \(a_{99}=+0.550784655\) \(a_{100}=+0.905359100\)

Showing 100 of 5000 available coefficients

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