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: \( 26.0195962906 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.333096992\) \(a_{3}=-0.577350269\) \(a_{4}=+0.777147591\) \(a_{5}=-1.642813430\)
\(a_{6}=+0.769663907\) \(a_{7}=-0.947530843\) \(a_{8}=+0.297083876\) \(a_{9}=+0.333333333\) \(a_{10}=+2.190029642\)
\(a_{11}=-1.045264746\) \(a_{12}=-0.448686371\) \(a_{13}=-1.035740858\) \(a_{14}=+1.263150517\) \(a_{15}=+0.948478776\)
\(a_{16}=-1.173189213\) \(a_{17}=+0.716741009\) \(a_{18}=-0.444365664\) \(a_{19}=+0.602845222\) \(a_{20}=-1.276708499\)
\(a_{21}=+0.547057187\) \(a_{22}=+1.393439290\) \(a_{23}=+1.353817745\) \(a_{24}=-0.171521456\) \(a_{25}=+1.698835965\)
\(a_{26}=+1.380743022\) \(a_{27}=-0.192450090\) \(a_{28}=-0.736371312\) \(a_{29}=+0.825771467\) \(a_{30}=-1.264414203\)
\(a_{31}=-0.331105248\) \(a_{32}=+1.266891135\) \(a_{33}=+0.603483883\) \(a_{34}=-0.955485283\) \(a_{35}=+1.556616394\)
\(a_{36}=+0.259049197\) \(a_{37}=+0.766697743\) \(a_{38}=-0.803651152\) \(a_{39}=+0.597985263\) \(a_{40}=-0.488053382\)
\(a_{41}=+0.889391159\) \(a_{42}=-0.729280291\) \(a_{43}=-1.199690809\) \(a_{44}=-0.812324980\) \(a_{45}=-0.547604477\)
\(a_{46}=-1.804770364\) \(a_{47}=+0.483991381\) \(a_{48}=+0.677341108\) \(a_{49}=-0.102185302\) \(a_{50}=-2.264713115\)
\(a_{51}=-0.413810614\) \(a_{52}=-0.804923512\) \(a_{53}=-1.267317496\) \(a_{54}=+0.256554636\) \(a_{55}=+1.717174963\)
\(a_{56}=-0.281496136\) \(a_{57}=-0.348052851\) \(a_{58}=-1.100833459\) \(a_{59}=-0.590221467\) \(a_{60}=+0.737107996\)
\(a_{61}=-0.982127323\) \(a_{62}=+0.441395410\) \(a_{63}=-0.315843614\) \(a_{64}=-0.515699549\) \(a_{65}=+1.701528991\)
\(a_{66}=-0.804502549\) \(a_{67}=+0.360372758\) \(a_{68}=+0.557013548\) \(a_{69}=-0.781627040\) \(a_{70}=-2.075120633\)
\(a_{71}=+1.566734648\) \(a_{72}=+0.099027959\) \(a_{73}=+1.106210552\) \(a_{74}=-1.022082455\) \(a_{75}=-0.980823402\)
\(a_{76}=+0.468499712\) \(a_{77}=+0.990420586\) \(a_{78}=-0.797172356\) \(a_{79}=-0.309220670\) \(a_{80}=+1.927330994\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.185644679\) \(a_{83}=-0.849156834\) \(a_{84}=+0.425144175\) \(a_{85}=-1.177471755\)
\(a_{86}=+1.599304210\) \(a_{87}=-0.476759379\) \(a_{88}=-0.310531303\) \(a_{89}=-0.569652007\) \(a_{90}=+0.730009881\)
\(a_{91}=+0.981396408\) \(a_{92}=+1.052116199\) \(a_{93}=+0.191163704\) \(a_{94}=-0.645207455\) \(a_{95}=-0.990362226\)
\(a_{96}=-0.731439938\) \(a_{97}=-1.196016047\) \(a_{98}=+0.136222919\) \(a_{99}=-0.348421582\) \(a_{100}=+1.320246278\)

Showing 100 of 1228 available coefficients

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