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: \( 1.24284670859 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.084943404\) \(a_{4}=+0.000000000\) \(a_{5}=-0.219138816\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.046458126\) \(a_{8}=+0.000000000\) \(a_{9}=-0.992784618\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.404552745\) \(a_{12}=+0.000000000\) \(a_{13}=+0.528590166\) \(a_{14}=+0.000000000\) \(a_{15}=+0.018614397\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+0.328396505\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.003946311\) \(a_{22}=+0.000000000\) \(a_{23}=+1.647337046\) \(a_{24}=+0.000000000\) \(a_{25}=-0.951978179\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.169273909\) \(a_{28}=+0.000000000\) \(a_{29}=-0.995659481\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.013468680\) \(a_{32}=+0.000000000\) \(a_{33}=-0.119307491\) \(a_{34}=+0.000000000\) \(a_{35}=-0.010180779\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.487903253\) \(a_{38}=+0.000000000\) \(a_{39}=-0.044900248\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.488425412\) \(a_{42}=+0.000000000\) \(a_{43}=-1.304263002\) \(a_{44}=+0.000000000\) \(a_{45}=+0.217557646\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.409812868\) \(a_{48}=+0.000000000\) \(a_{49}=-0.997841643\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.020601802\) \(a_{52}=+0.000000000\) \(a_{53}=+1.526251411\) \(a_{54}=+0.000000000\) \(a_{55}=-0.307792025\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.027895117\) \(a_{58}=+0.000000000\) \(a_{59}=+1.290153546\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.782167148\) \(a_{62}=+0.000000000\) \(a_{63}=-0.046122912\) \(a_{64}=+0.000000000\) \(a_{65}=-0.115834623\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.885837492\) \(a_{68}=+0.000000000\) \(a_{69}=-0.139930416\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.088612433\) \(a_{72}=+0.000000000\) \(a_{73}=+1.696693660\) \(a_{74}=+0.000000000\) \(a_{75}=+0.080864267\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.065252888\) \(a_{78}=+0.000000000\) \(a_{79}=-0.871633397\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.978405916\) \(a_{82}=+0.000000000\) \(a_{83}=-1.255564764\) \(a_{84}=+0.000000000\) \(a_{85}=-0.053148970\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.084574705\) \(a_{88}=+0.000000000\) \(a_{89}=-1.186185685\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.024557308\) \(a_{92}=+0.000000000\) \(a_{93}=+0.086087479\) \(a_{94}=+0.000000000\) \(a_{95}=-0.071964421\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.029889920\) \(a_{98}=+0.000000000\) \(a_{99}=-1.394418360\) \(a_{100}=+0.000000000\)

Showing 100 of 642 available coefficients

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