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: \( 16.9905650919 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.591878150\) \(a_{3}=+0.577350269\) \(a_{4}=+1.534076045\) \(a_{5}=+1.841285600\)
\(a_{6}=+0.919071279\) \(a_{7}=-0.586326532\) \(a_{8}=+0.850183987\) \(a_{9}=+0.333333333\) \(a_{10}=+2.931102315\)
\(a_{11}=-0.065337396\) \(a_{12}=+0.885699218\) \(a_{13}=-0.623733479\) \(a_{14}=-0.933360395\) \(a_{15}=+1.063066737\)
\(a_{16}=-0.180686733\) \(a_{17}=+0.596731707\) \(a_{18}=+0.530626050\) \(a_{19}=+0.127924924\) \(a_{20}=+2.824672132\)
\(a_{21}=-0.338515781\) \(a_{22}=-0.104009173\) \(a_{23}=-0.253874852\) \(a_{24}=+0.490853954\) \(a_{25}=+2.390332661\)
\(a_{26}=-0.992907697\) \(a_{27}=+0.192450090\) \(a_{28}=-0.899469488\) \(a_{29}=-0.672606298\) \(a_{30}=+1.692272711\)
\(a_{31}=+0.670276402\) \(a_{32}=-1.137815249\) \(a_{33}=-0.037722563\) \(a_{34}=+0.949924166\) \(a_{35}=-1.079594601\)
\(a_{36}=+0.511358682\) \(a_{37}=-0.537012261\) \(a_{38}=+0.203640892\) \(a_{39}=-0.360112692\) \(a_{40}=+1.565431533\)
\(a_{41}=-0.936601304\) \(a_{42}=-0.538875876\) \(a_{43}=+0.809994598\) \(a_{44}=-0.100232534\) \(a_{45}=+0.613761867\)
\(a_{46}=-0.404137831\) \(a_{47}=-1.726434842\) \(a_{48}=-0.104319534\) \(a_{49}=-0.656221198\) \(a_{50}=+3.805118335\)
\(a_{51}=+0.344523212\) \(a_{52}=-0.956854589\) \(a_{53}=-1.562628720\) \(a_{54}=+0.306357093\) \(a_{55}=-0.120304807\)
\(a_{56}=-0.498485429\) \(a_{57}=+0.073857490\) \(a_{58}=-1.070707270\) \(a_{59}=+1.463944981\) \(a_{60}=+1.630825216\)
\(a_{61}=-0.882563514\) \(a_{62}=+1.066998360\) \(a_{63}=-0.195442177\) \(a_{64}=-1.630576501\) \(a_{65}=-1.148471474\)
\(a_{66}=-0.060049724\) \(a_{67}=+1.357964045\) \(a_{68}=+0.915431817\) \(a_{69}=-0.146574714\) \(a_{70}=-1.718583056\)
\(a_{71}=+1.081202867\) \(a_{72}=+0.283394662\) \(a_{73}=-0.295205425\) \(a_{74}=-0.854858084\) \(a_{75}=+1.380059205\)
\(a_{76}=+0.196246562\) \(a_{77}=+0.038309049\) \(a_{78}=-0.573255526\) \(a_{79}=+0.284092978\) \(a_{80}=-0.332695879\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.490955151\) \(a_{83}=+0.181114950\) \(a_{84}=-0.519308951\) \(a_{85}=+1.098753499\)
\(a_{86}=+1.289412702\) \(a_{87}=-0.388329427\) \(a_{88}=-0.055548808\) \(a_{89}=-0.241899648\) \(a_{90}=+0.977034105\)
\(a_{91}=+0.365711488\) \(a_{92}=-0.389463330\) \(a_{93}=+0.386984261\) \(a_{94}=-2.748273903\) \(a_{95}=+0.235546321\)
\(a_{96}=-0.656917940\) \(a_{97}=+0.581669811\) \(a_{98}=-1.044624186\) \(a_{99}=-0.021779132\) \(a_{100}=+3.666952076\)

Showing 100 of 1228 available coefficients

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