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: \( 13.9931761916 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.641668640\) \(a_{3}=+0.577350269\) \(a_{4}=-0.588261357\) \(a_{5}=+0.232300686\)
\(a_{6}=-0.370467562\) \(a_{7}=+0.499113330\) \(a_{8}=+1.019137504\) \(a_{9}=+0.333333333\) \(a_{10}=-0.149060065\)
\(a_{11}=-0.346275690\) \(a_{12}=-0.339632853\) \(a_{13}=-1.955993299\) \(a_{14}=-0.320265372\) \(a_{15}=+0.134118864\)
\(a_{16}=-0.065687219\) \(a_{17}=-1.396313152\) \(a_{18}=-0.213889547\) \(a_{19}=+0.471632367\) \(a_{20}=-0.136653517\)
\(a_{21}=+0.288163215\) \(a_{22}=+0.222194251\) \(a_{23}=-1.198334326\) \(a_{24}=+0.588399312\) \(a_{25}=-0.946036391\)
\(a_{26}=+1.255099559\) \(a_{27}=+0.192450090\) \(a_{28}=-0.293609085\) \(a_{29}=-0.275863348\) \(a_{30}=-0.086059869\)
\(a_{31}=+0.520582417\) \(a_{32}=-0.976988076\) \(a_{33}=-0.199922363\) \(a_{34}=+0.895970361\) \(a_{35}=+0.115944369\)
\(a_{36}=-0.196087119\) \(a_{37}=+0.933200942\) \(a_{38}=-0.302631699\) \(a_{39}=-1.129293258\) \(a_{40}=+0.236746342\)
\(a_{41}=-0.782941345\) \(a_{42}=-0.184905298\) \(a_{43}=+1.516362106\) \(a_{44}=+0.203700607\) \(a_{45}=+0.077433562\)
\(a_{46}=+0.768933557\) \(a_{47}=-1.408589507\) \(a_{48}=-0.037924534\) \(a_{49}=-0.750885884\) \(a_{50}=+0.607041884\)
\(a_{51}=-0.806161774\) \(a_{52}=+1.150635272\) \(a_{53}=-0.027885356\) \(a_{54}=-0.123489187\) \(a_{55}=-0.080440080\)
\(a_{56}=+0.508665113\) \(a_{57}=+0.272297074\) \(a_{58}=+0.177012859\) \(a_{59}=-0.786920222\) \(a_{60}=-0.078896945\)
\(a_{61}=-0.469006967\) \(a_{62}=-0.334041412\) \(a_{63}=+0.166371110\) \(a_{64}=+0.692589829\) \(a_{65}=-0.454378586\)
\(a_{66}=+0.128283911\) \(a_{67}=+0.370053848\) \(a_{68}=+0.821397069\) \(a_{69}=-0.691858646\) \(a_{70}=-0.074397866\)
\(a_{71}=+0.735672379\) \(a_{72}=+0.339712501\) \(a_{73}=-1.095238888\) \(a_{74}=-0.598805779\) \(a_{75}=-0.546194365\)
\(a_{76}=-0.277443096\) \(a_{77}=-0.172830813\) \(a_{78}=+0.724632069\) \(a_{79}=+1.252944892\) \(a_{80}=-0.015259186\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.502388908\) \(a_{83}=-0.082386890\) \(a_{84}=-0.169515284\) \(a_{85}=-0.324364503\)
\(a_{86}=-0.973002010\) \(a_{87}=-0.159269778\) \(a_{88}=-0.352902542\) \(a_{89}=+0.742294871\) \(a_{90}=-0.049686688\)
\(a_{91}=-0.976262329\) \(a_{92}=+0.704933777\) \(a_{93}=+0.300558399\) \(a_{94}=+0.903847713\) \(a_{95}=+0.109560522\)
\(a_{96}=-0.564064329\) \(a_{97}=-0.387441384\) \(a_{98}=+0.481819924\) \(a_{99}=-0.115425230\) \(a_{100}=+0.556516651\)

Showing 100 of 1228 available coefficients

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