Properties

Level $8$
Weight $0$
Character 8.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 14.988459734 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.813970659\) \(a_{4}=+0.000000000\) \(a_{5}=-0.558383583\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.357702770\) \(a_{8}=+0.000000000\) \(a_{9}=+2.290489552\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.663480591\) \(a_{12}=+0.000000000\) \(a_{13}=-1.296884609\) \(a_{14}=+0.000000000\) \(a_{15}=-1.012891436\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.478670366\) \(a_{18}=+0.000000000\) \(a_{19}=-0.922604759\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.648862329\) \(a_{22}=+0.000000000\) \(a_{23}=+0.709067505\) \(a_{24}=+0.000000000\) \(a_{25}=-0.688207774\)
\(a_{26}=+0.000000000\) \(a_{27}=+2.340910184\) \(a_{28}=+0.000000000\) \(a_{29}=-0.054090642\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.571427628\) \(a_{32}=+0.000000000\) \(a_{33}=-3.017504986\) \(a_{34}=+0.000000000\) \(a_{35}=+0.199735354\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.202225659\) \(a_{38}=+0.000000000\) \(a_{39}=-2.352510619\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.383978775\) \(a_{42}=+0.000000000\) \(a_{43}=-0.658652601\) \(a_{44}=+0.000000000\) \(a_{45}=-1.278971776\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.634416595\) \(a_{48}=+0.000000000\) \(a_{49}=-0.872046373\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.868277577\) \(a_{52}=+0.000000000\) \(a_{53}=+0.552827756\) \(a_{54}=+0.000000000\) \(a_{55}=+0.928890027\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.673915654\) \(a_{58}=+0.000000000\) \(a_{59}=-0.277944717\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.394501750\) \(a_{62}=+0.000000000\) \(a_{63}=-0.827887477\) \(a_{64}=+0.000000000\) \(a_{65}=+0.697222203\)
\(a_{66}=+0.000000000\)

Showing all 66 available coefficients

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