Properties

Level $68$
Weight $0$
Character 68.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 68 = 2^{2} \cdot 17 \)
Weight: \( 0 \)
Character: 68.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 5.11227601689 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.929523556\) \(a_{4}=+0.000000000\) \(a_{5}=-0.229487713\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.753630682\) \(a_{8}=+0.000000000\) \(a_{9}=+2.723061152\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.383573567\) \(a_{12}=+0.000000000\) \(a_{13}=+0.446325481\) \(a_{14}=+0.000000000\) \(a_{15}=+0.442801948\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+0.305690351\) \(a_{20}=+0.000000000\)
\(a_{21}=+3.383671710\) \(a_{22}=+0.000000000\) \(a_{23}=-0.440807856\) \(a_{24}=+0.000000000\) \(a_{25}=-0.947335390\)
\(a_{26}=+0.000000000\) \(a_{27}=-3.324687081\) \(a_{28}=+0.000000000\) \(a_{29}=+1.826822481\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.662037800\) \(a_{32}=+0.000000000\) \(a_{33}=-2.669637789\) \(a_{34}=+0.000000000\) \(a_{35}=+0.402436695\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.266949480\) \(a_{38}=+0.000000000\) \(a_{39}=-0.861195530\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.325888391\) \(a_{42}=+0.000000000\) \(a_{43}=-0.894581715\) \(a_{44}=+0.000000000\) \(a_{45}=-0.624909076\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.118361085\) \(a_{48}=+0.000000000\) \(a_{49}=+2.075220570\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.467978202\) \(a_{52}=+0.000000000\) \(a_{53}=+1.014640782\) \(a_{54}=+0.000000000\) \(a_{55}=-0.317513134\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.589836733\) \(a_{58}=+0.000000000\) \(a_{59}=-0.304550635\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.880583155\) \(a_{62}=+0.000000000\) \(a_{63}=-4.775243587\) \(a_{64}=+0.000000000\) \(a_{65}=-0.102426214\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.022781428\) \(a_{68}=+0.000000000\) \(a_{69}=+0.850549142\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.528008482\) \(a_{72}=+0.000000000\) \(a_{73}=-0.435270741\) \(a_{74}=+0.000000000\) \(a_{75}=+1.827905950\)
\(a_{76}=+0.000000000\) \(a_{77}=-2.426277058\) \(a_{78}=+0.000000000\) \(a_{79}=-0.222918091\) \(a_{80}=+0.000000000\)
\(a_{81}=+3.692000887\) \(a_{82}=+0.000000000\) \(a_{83}=+0.874204658\) \(a_{84}=+0.000000000\) \(a_{85}=-0.055658946\)
\(a_{86}=+0.000000000\) \(a_{87}=-3.524897010\) \(a_{88}=+0.000000000\) \(a_{89}=+0.133029474\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.782690059\) \(a_{92}=+0.000000000\) \(a_{93}=+1.277417530\) \(a_{94}=+0.000000000\) \(a_{95}=-0.070152180\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.233912592\) \(a_{98}=+0.000000000\) \(a_{99}=+3.767555432\) \(a_{100}=+0.000000000\)

Showing 100 of 630 available coefficients

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