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: \( 6.32531406199 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.512848902\) \(a_{4}=+0.000000000\) \(a_{5}=+1.255040834\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.508658008\) \(a_{8}=+0.000000000\) \(a_{9}=+1.288711801\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.007841281\) \(a_{12}=+0.000000000\) \(a_{13}=+0.847980142\) \(a_{14}=+0.000000000\) \(a_{15}=-1.898687147\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.192910276\) \(a_{18}=+0.000000000\) \(a_{19}=+1.244208893\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.769522709\) \(a_{22}=+0.000000000\) \(a_{23}=-1.054124754\) \(a_{24}=+0.000000000\) \(a_{25}=+0.575127494\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.436777332\) \(a_{28}=+0.000000000\) \(a_{29}=+0.524478687\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.380700821\) \(a_{32}=+0.000000000\) \(a_{33}=+0.011862673\) \(a_{34}=+0.000000000\) \(a_{35}=+0.638386570\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.610186631\) \(a_{38}=+0.000000000\) \(a_{39}=-1.282865827\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.844051767\) \(a_{42}=+0.000000000\) \(a_{43}=+0.980382632\) \(a_{44}=+0.000000000\) \(a_{45}=+1.617385933\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.615962883\) \(a_{48}=+0.000000000\) \(a_{49}=-0.741267031\) \(a_{50}=+0.000000000\)
\(a_{51}=-1.804693002\) \(a_{52}=+0.000000000\) \(a_{53}=+1.874027435\) \(a_{54}=+0.000000000\) \(a_{55}=-0.009841127\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.882300058\) \(a_{58}=+0.000000000\) \(a_{59}=+0.916385838\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.336535915\) \(a_{62}=+0.000000000\) \(a_{63}=+0.655513578\) \(a_{64}=+0.000000000\) \(a_{65}=+1.064249705\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.079068858\) \(a_{68}=+0.000000000\) \(a_{69}=+1.594731473\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.015024025\) \(a_{72}=+0.000000000\) \(a_{73}=-1.099511566\) \(a_{74}=+0.000000000\) \(a_{75}=-0.870080998\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.003988530\) \(a_{78}=+0.000000000\) \(a_{79}=-1.050007242\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.627933694\) \(a_{82}=+0.000000000\) \(a_{83}=+1.404053095\) \(a_{84}=+0.000000000\) \(a_{85}=+1.497151107\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.793457006\) \(a_{88}=+0.000000000\) \(a_{89}=-0.518739013\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.431331890\) \(a_{92}=+0.000000000\) \(a_{93}=-0.575942819\) \(a_{94}=+0.000000000\) \(a_{95}=+1.561532966\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.743667617\) \(a_{98}=+0.000000000\) \(a_{99}=-0.010105153\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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