Properties

Level $6$
Weight $0$
Character 6.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 13.6987468059 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.155613829\)
\(a_{6}=-0.408248290\) \(a_{7}=+1.338155508\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.817142375\)
\(a_{11}=-0.939655664\) \(a_{12}=+0.288675135\) \(a_{13}=+0.184793843\) \(a_{14}=-0.946218834\) \(a_{15}=-0.667193956\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.441333133\) \(a_{18}=-0.235702260\) \(a_{19}=+0.737070828\) \(a_{20}=-0.577806915\)
\(a_{21}=+0.772584443\) \(a_{22}=+0.664436892\) \(a_{23}=+1.534540746\) \(a_{24}=-0.204124145\) \(a_{25}=+0.335443323\)
\(a_{26}=-0.130668979\) \(a_{27}=+0.192450090\) \(a_{28}=+0.669077753\) \(a_{29}=+1.678584905\) \(a_{30}=+0.471777373\)
\(a_{31}=+0.177369323\) \(a_{32}=-0.176776686\) \(a_{33}=-0.542510418\) \(a_{34}=+1.019176309\) \(a_{35}=-1.546391011\)
\(a_{36}=+0.166666667\) \(a_{37}=+1.338464708\) \(a_{38}=-0.521187781\) \(a_{39}=+0.106690775\) \(a_{40}=+0.408571188\)
\(a_{41}=+1.317259574\) \(a_{42}=-0.546299698\) \(a_{43}=-0.125854699\) \(a_{44}=-0.469827832\) \(a_{45}=-0.385204610\)
\(a_{46}=-1.085084167\) \(a_{47}=+0.786483777\) \(a_{48}=+0.144337567\) \(a_{49}=+0.790660163\) \(a_{50}=-0.237194248\)
\(a_{51}=-0.832154072\) \(a_{52}=+0.092396921\) \(a_{53}=+0.878331543\) \(a_{54}=-0.136082764\) \(a_{55}=+1.085879080\)
\(a_{56}=-0.473109417\) \(a_{57}=+0.425548041\) \(a_{58}=-1.186938769\) \(a_{59}=-0.405766783\) \(a_{60}=-0.333596977\)
\(a_{61}=+0.313991060\) \(a_{62}=-0.125419058\) \(a_{63}=+0.446051835\) \(a_{64}=+0.125000001\) \(a_{65}=-0.213550320\)
\(a_{66}=+0.383612817\) \(a_{67}=-0.589076230\) \(a_{68}=-0.720666564\) \(a_{69}=+0.885967510\) \(a_{70}=+1.093463568\)
\(a_{71}=-0.845655722\) \(a_{72}=-0.117851129\) \(a_{73}=+1.853250282\) \(a_{74}=-0.946437472\) \(a_{75}=+0.193668366\)
\(a_{76}=+0.368535400\) \(a_{77}=-1.257405402\) \(a_{78}=-0.075441770\) \(a_{79}=-0.928490776\) \(a_{80}=-0.288903457\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.931443178\) \(a_{83}=+0.331881907\) \(a_{84}=+0.386292221\) \(a_{85}=+1.665624502\)
\(a_{86}=+0.088992711\) \(a_{87}=+0.969131447\) \(a_{88}=+0.332218446\) \(a_{89}=-1.685284466\) \(a_{90}=+0.272380792\)
\(a_{91}=+0.247282899\) \(a_{92}=+0.767270373\) \(a_{93}=+0.102404232\) \(a_{94}=-0.556128012\) \(a_{95}=-0.851769242\)
\(a_{96}=-0.102062073\) \(a_{97}=-0.674252089\) \(a_{98}=-0.559081163\) \(a_{99}=-0.313218554\) \(a_{100}=+0.167721660\)

Showing 100 of 1000 available coefficients

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