Properties

Level $61$
Weight $0$
Character 61.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 61 \)
Weight: \( 0 \)
Character: 61.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.41806231115 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.769503671\) \(a_{3}=+0.145641226\) \(a_{4}=-0.407864101\) \(a_{5}=+0.621591987\)
\(a_{6}=+0.112071458\) \(a_{7}=+0.503602262\) \(a_{8}=-1.083356593\) \(a_{9}=-0.978788633\) \(a_{10}=+0.478317316\)
\(a_{11}=-1.346908561\) \(a_{12}=-0.059401828\) \(a_{13}=+0.819490170\) \(a_{14}=+0.387523789\) \(a_{15}=+0.090529419\)
\(a_{16}=-0.425782774\) \(a_{17}=+0.488697692\) \(a_{18}=-0.753181446\) \(a_{19}=+0.525479096\) \(a_{20}=-0.253525057\)
\(a_{21}=+0.073345251\) \(a_{22}=-1.036451082\) \(a_{23}=+1.081205383\) \(a_{24}=-0.157781382\) \(a_{25}=-0.613623401\)
\(a_{26}=+0.630600694\) \(a_{27}=-0.288193202\) \(a_{28}=-0.205401284\) \(a_{29}=+0.727766535\) \(a_{30}=+0.069662720\)
\(a_{31}=+0.258047543\) \(a_{32}=+0.755715186\) \(a_{33}=-0.196165414\) \(a_{34}=+0.376054668\) \(a_{35}=+0.313035131\)
\(a_{36}=+0.399212746\) \(a_{37}=-0.625946336\) \(a_{38}=+0.404358093\) \(a_{39}=+0.119351553\) \(a_{40}=-0.673405778\)
\(a_{41}=-0.287948013\) \(a_{42}=+0.056439440\) \(a_{43}=+0.596778753\) \(a_{44}=+0.549355649\) \(a_{45}=-0.608407172\)
\(a_{46}=+0.831991511\) \(a_{47}=+0.432520623\) \(a_{48}=-0.062011525\) \(a_{49}=-0.746384761\) \(a_{50}=-0.472185460\)
\(a_{51}=+0.071174531\) \(a_{52}=-0.334240622\) \(a_{53}=-0.601407765\) \(a_{54}=-0.221765727\) \(a_{55}=-0.837227569\)
\(a_{56}=-0.545580831\) \(a_{57}=+0.076531420\) \(a_{58}=+0.560019020\) \(a_{59}=-0.725962877\) \(a_{60}=-0.036923700\)
\(a_{61}=+0.128036880\) \(a_{62}=+0.198568532\) \(a_{63}=-0.492920170\) \(a_{64}=+1.007308384\) \(a_{65}=+0.509388524\)
\(a_{66}=-0.150950006\) \(a_{67}=-0.833082536\) \(a_{68}=-0.199322245\) \(a_{69}=+0.157468077\) \(a_{70}=+0.240881682\)
\(a_{71}=-1.051878510\) \(a_{72}=+1.060377119\) \(a_{73}=-1.533192831\) \(a_{74}=-0.481668003\) \(a_{75}=-0.089368864\)
\(a_{76}=-0.214324059\) \(a_{77}=-0.678306199\) \(a_{78}=+0.091841458\) \(a_{79}=+0.442891182\) \(a_{80}=-0.264663161\)
\(a_{81}=+0.936815822\) \(a_{82}=-0.221577053\) \(a_{83}=+1.922363610\) \(a_{84}=-0.029914895\) \(a_{85}=+0.303770570\)
\(a_{86}=+0.459223441\) \(a_{87}=+0.105992810\) \(a_{88}=+1.459182271\) \(a_{89}=+1.424155351\) \(a_{90}=-0.468171552\)
\(a_{91}=+0.412697104\) \(a_{92}=-0.440984861\) \(a_{93}=+0.037582360\) \(a_{94}=+0.332826207\) \(a_{95}=+0.326633596\)
\(a_{96}=+0.110063286\) \(a_{97}=-0.711605950\) \(a_{98}=-0.574345814\) \(a_{99}=+1.318338790\) \(a_{100}=+0.250274957\)

Showing 100 of 546 available coefficients

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