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: \( 2.6561659023 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.533112790\) \(a_{4}=+0.000000000\) \(a_{5}=-0.821039304\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.327188292\) \(a_{8}=+0.000000000\) \(a_{9}=-0.715790753\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.561238299\) \(a_{12}=+0.000000000\) \(a_{13}=-0.805192237\) \(a_{14}=+0.000000000\) \(a_{15}=-0.437706555\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+0.881498359\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.707541054\) \(a_{22}=+0.000000000\) \(a_{23}=-1.938308506\) \(a_{24}=+0.000000000\) \(a_{25}=-0.325894461\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.914709996\) \(a_{28}=+0.000000000\) \(a_{29}=+1.105493848\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.255909576\) \(a_{32}=+0.000000000\) \(a_{33}=+0.832316106\) \(a_{34}=+0.000000000\) \(a_{35}=+1.089673752\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.038045646\) \(a_{38}=+0.000000000\) \(a_{39}=-0.429258280\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.109918556\) \(a_{42}=+0.000000000\) \(a_{43}=+0.964884051\) \(a_{44}=+0.000000000\) \(a_{45}=+0.587692342\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.299534872\) \(a_{48}=+0.000000000\) \(a_{49}=+0.761428763\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.129298844\) \(a_{52}=+0.000000000\) \(a_{53}=+0.266347679\) \(a_{54}=+0.000000000\) \(a_{55}=-1.281838007\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.469938050\) \(a_{58}=+0.000000000\) \(a_{59}=-1.097646217\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.116469312\) \(a_{62}=+0.000000000\) \(a_{63}=+0.949989107\) \(a_{64}=+0.000000000\) \(a_{65}=+0.661094474\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.727273065\) \(a_{68}=+0.000000000\) \(a_{69}=-1.033337056\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.143977459\) \(a_{72}=+0.000000000\) \(a_{73}=-0.518355935\) \(a_{74}=+0.000000000\) \(a_{75}=-0.173738505\)
\(a_{76}=+0.000000000\) \(a_{77}=-2.072057192\) \(a_{78}=+0.000000000\) \(a_{79}=+1.560592445\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.228147154\) \(a_{82}=+0.000000000\) \(a_{83}=-0.698787257\) \(a_{84}=+0.000000000\) \(a_{85}=+0.199131281\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.589352910\) \(a_{88}=+0.000000000\) \(a_{89}=+0.851417266\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.068641710\) \(a_{92}=+0.000000000\) \(a_{93}=-0.669541459\) \(a_{94}=+0.000000000\) \(a_{95}=-0.723744799\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.077470023\) \(a_{98}=+0.000000000\) \(a_{99}=-1.117519937\) \(a_{100}=+0.000000000\)

Showing 100 of 556 available coefficients

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