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: \( 4.77254315238 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.939208786\) \(a_{4}=+0.000000000\) \(a_{5}=+0.092026447\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.394697066\) \(a_{8}=+0.000000000\) \(a_{9}=-0.117886856\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.725648949\) \(a_{12}=+0.000000000\) \(a_{13}=-1.512738753\) \(a_{14}=+0.000000000\) \(a_{15}=-0.086432048\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+0.657568560\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.309911738\) \(a_{22}=+0.000000000\) \(a_{23}=-0.124292268\) \(a_{24}=+0.000000000\) \(a_{25}=-0.991531133\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.049929157\) \(a_{28}=+0.000000000\) \(a_{29}=-1.061593058\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.193006899\) \(a_{32}=+0.000000000\) \(a_{33}=+0.681535868\) \(a_{34}=+0.000000000\) \(a_{35}=-0.128349016\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.240831705\) \(a_{38}=+0.000000000\) \(a_{39}=+1.420777528\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.015258287\) \(a_{42}=+0.000000000\) \(a_{43}=+1.684539055\) \(a_{44}=+0.000000000\) \(a_{45}=-0.010848709\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.142513335\) \(a_{48}=+0.000000000\) \(a_{49}=+0.945179905\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.227791590\) \(a_{52}=+0.000000000\) \(a_{53}=+1.818485029\) \(a_{54}=+0.000000000\) \(a_{55}=-0.066778895\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.617594169\) \(a_{58}=+0.000000000\) \(a_{59}=-1.167198706\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.842029591\) \(a_{62}=+0.000000000\) \(a_{63}=+0.164416452\) \(a_{64}=+0.000000000\) \(a_{65}=-0.139211973\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.359077908\) \(a_{68}=+0.000000000\) \(a_{69}=+0.116736391\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.088779363\) \(a_{72}=+0.000000000\) \(a_{73}=-0.415663939\) \(a_{74}=+0.000000000\) \(a_{75}=+0.931254752\)
\(a_{76}=+0.000000000\) \(a_{77}=+1.012060460\) \(a_{78}=+0.000000000\) \(a_{79}=+1.730774915\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.868215833\) \(a_{82}=+0.000000000\) \(a_{83}=-0.922833440\) \(a_{84}=+0.000000000\) \(a_{85}=+0.022319692\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.997057527\) \(a_{88}=+0.000000000\) \(a_{89}=-1.078955649\) \(a_{90}=+0.000000000\)
\(a_{91}=+2.109812299\) \(a_{92}=+0.000000000\) \(a_{93}=-1.120482562\) \(a_{94}=+0.000000000\) \(a_{95}=+0.060513698\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.321960676\) \(a_{98}=+0.000000000\) \(a_{99}=+0.085544473\) \(a_{100}=+0.000000000\)

Showing 100 of 618 available coefficients

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