Properties

Level $68$
Weight $0$
Character 68.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 68 = 2^{2} \cdot 17 \)
Weight: \( 0 \)
Character: 68.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 2.07484902684 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.759908382\) \(a_{4}=+0.000000000\) \(a_{5}=+1.175411277\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.226526684\) \(a_{8}=+0.000000000\) \(a_{9}=+2.097277512\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.140538457\) \(a_{12}=+0.000000000\) \(a_{13}=-1.550748848\) \(a_{14}=+0.000000000\) \(a_{15}=-2.068616158\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-0.924499808\) \(a_{20}=+0.000000000\)
\(a_{21}=+2.158574592\) \(a_{22}=+0.000000000\) \(a_{23}=+1.035793326\) \(a_{24}=+0.000000000\) \(a_{25}=+0.381591669\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.931107891\) \(a_{28}=+0.000000000\) \(a_{29}=-1.028500717\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.527826596\) \(a_{32}=+0.000000000\) \(a_{33}=-0.247334809\) \(a_{34}=+0.000000000\) \(a_{35}=-1.441673296\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.487728817\) \(a_{38}=+0.000000000\) \(a_{39}=+2.729175895\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.542326366\) \(a_{42}=+0.000000000\) \(a_{43}=-1.273414717\) \(a_{44}=+0.000000000\) \(a_{45}=+2.465163638\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.577817715\) \(a_{48}=+0.000000000\) \(a_{49}=+0.504367707\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.426840479\) \(a_{52}=+0.000000000\) \(a_{53}=-0.879424400\) \(a_{54}=+0.000000000\) \(a_{55}=+0.165190488\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.627034960\) \(a_{58}=+0.000000000\) \(a_{59}=+0.512884569\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.444044729\) \(a_{62}=+0.000000000\) \(a_{63}=-2.572366833\) \(a_{64}=+0.000000000\) \(a_{65}=-1.822767683\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.737508757\) \(a_{68}=+0.000000000\) \(a_{69}=-1.822901356\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.897484973\) \(a_{72}=+0.000000000\) \(a_{73}=-1.449916581\) \(a_{74}=+0.000000000\) \(a_{75}=-0.671566377\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.172374168\) \(a_{78}=+0.000000000\) \(a_{79}=+0.204448211\) \(a_{80}=+0.000000000\)
\(a_{81}=+1.301295451\) \(a_{82}=+0.000000000\) \(a_{83}=-1.210765917\) \(a_{84}=+0.000000000\) \(a_{85}=-0.285079109\)
\(a_{86}=+0.000000000\) \(a_{87}=+1.810067032\) \(a_{88}=+0.000000000\) \(a_{89}=+0.758240198\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.902034842\) \(a_{92}=+0.000000000\) \(a_{93}=-0.928926451\) \(a_{94}=+0.000000000\) \(a_{95}=-1.086667499\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.252647277\) \(a_{98}=+0.000000000\) \(a_{99}=+0.294748146\) \(a_{100}=+0.000000000\)

Showing 100 of 640 available coefficients

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