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: \( 2.42505682709 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.294048038\) \(a_{4}=+0.000000000\) \(a_{5}=+0.906835855\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.386145032\) \(a_{8}=+0.000000000\) \(a_{9}=-0.913535752\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.711588675\) \(a_{12}=+0.000000000\) \(a_{13}=+0.704671668\) \(a_{14}=+0.000000000\) \(a_{15}=-0.266653304\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.113362807\) \(a_{18}=+0.000000000\) \(a_{19}=-1.234244324\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.113545189\) \(a_{22}=+0.000000000\) \(a_{23}=+1.392002461\) \(a_{24}=+0.000000000\) \(a_{25}=-0.177648730\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.562671433\) \(a_{28}=+0.000000000\) \(a_{29}=-0.395727480\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.990268936\) \(a_{32}=+0.000000000\) \(a_{33}=-0.209241253\) \(a_{34}=+0.000000000\) \(a_{35}=-0.350170160\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.024879809\) \(a_{38}=+0.000000000\) \(a_{39}=-0.207207321\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.615645000\) \(a_{42}=+0.000000000\) \(a_{43}=+1.222502484\) \(a_{44}=+0.000000000\) \(a_{45}=-0.828426955\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.709807867\) \(a_{48}=+0.000000000\) \(a_{49}=-0.850892050\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.033334539\) \(a_{52}=+0.000000000\) \(a_{53}=-0.335524177\) \(a_{54}=+0.000000000\) \(a_{55}=+0.645294391\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.362922608\) \(a_{58}=+0.000000000\) \(a_{59}=-0.269785384\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.104346502\) \(a_{62}=+0.000000000\) \(a_{63}=+0.352819261\) \(a_{64}=+0.000000000\) \(a_{65}=+0.638523316\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.739191247\) \(a_{68}=+0.000000000\) \(a_{69}=-0.409315590\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.508227278\) \(a_{72}=+0.000000000\) \(a_{73}=-1.152911680\) \(a_{74}=+0.000000000\) \(a_{75}=+0.052237149\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.274776182\) \(a_{78}=+0.000000000\) \(a_{79}=+0.287122187\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.748082869\) \(a_{82}=+0.000000000\) \(a_{83}=+1.333974076\) \(a_{84}=+0.000000000\) \(a_{85}=-0.102800885\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.116345438\) \(a_{88}=+0.000000000\) \(a_{89}=-0.409164282\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.272101215\) \(a_{92}=+0.000000000\) \(a_{93}=+0.291177724\) \(a_{94}=+0.000000000\) \(a_{95}=-1.119037870\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.389612056\) \(a_{98}=+0.000000000\) \(a_{99}=-0.650261338\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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