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: \( 5.52890067235 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.966519283\) \(a_{4}=+0.000000000\) \(a_{5}=+0.870065982\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.260390004\) \(a_{8}=+0.000000000\) \(a_{9}=+2.867198091\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.012633015\) \(a_{12}=+0.000000000\) \(a_{13}=+1.422665802\) \(a_{14}=+0.000000000\) \(a_{15}=+1.711001531\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=-0.111761249\) \(a_{20}=+0.000000000\)
\(a_{21}=-2.478581248\) \(a_{22}=+0.000000000\) \(a_{23}=+1.155808596\) \(a_{24}=+0.000000000\) \(a_{25}=-0.242985187\)
\(a_{26}=+0.000000000\) \(a_{27}=+3.671881052\) \(a_{28}=+0.000000000\) \(a_{29}=+1.041744746\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.031631104\) \(a_{32}=+0.000000000\) \(a_{33}=+0.024843068\) \(a_{34}=+0.000000000\) \(a_{35}=-1.096622467\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.505516689\) \(a_{38}=+0.000000000\) \(a_{39}=+2.797699733\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.255003813\) \(a_{42}=+0.000000000\) \(a_{43}=+1.306155979\) \(a_{44}=+0.000000000\) \(a_{45}=+2.494651522\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.658357499\) \(a_{48}=+0.000000000\) \(a_{49}=+0.588582963\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.476950983\) \(a_{52}=+0.000000000\) \(a_{53}=-0.117843867\) \(a_{54}=+0.000000000\) \(a_{55}=+0.010991557\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.219780651\) \(a_{58}=+0.000000000\) \(a_{59}=+0.307393243\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.574550788\) \(a_{62}=+0.000000000\) \(a_{63}=-3.613787815\) \(a_{64}=+0.000000000\) \(a_{65}=+1.237813117\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.714334454\) \(a_{68}=+0.000000000\) \(a_{69}=+2.272919891\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.950559037\) \(a_{72}=+0.000000000\) \(a_{73}=-1.304073408\) \(a_{74}=+0.000000000\) \(a_{75}=-0.477835057\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.015922526\) \(a_{78}=+0.000000000\) \(a_{79}=+1.379352271\) \(a_{80}=+0.000000000\)
\(a_{81}=+4.353626804\) \(a_{82}=+0.000000000\) \(a_{83}=+0.521463285\) \(a_{84}=+0.000000000\) \(a_{85}=-0.211021997\)
\(a_{86}=+0.000000000\) \(a_{87}=+2.048611130\) \(a_{88}=+0.000000000\) \(a_{89}=-1.813155656\) \(a_{90}=+0.000000000\)
\(a_{91}=-1.793113756\) \(a_{92}=+0.000000000\) \(a_{93}=+0.062203176\) \(a_{94}=+0.000000000\) \(a_{95}=-0.097239661\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.896799690\) \(a_{98}=+0.000000000\) \(a_{99}=+0.036221357\) \(a_{100}=+0.000000000\)

Showing 100 of 672 available coefficients

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