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: \( 11.4814591662 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.624829246\) \(a_{4}=+0.000000000\) \(a_{5}=-0.452228335\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.411864352\) \(a_{8}=+0.000000000\) \(a_{9}=-0.609588413\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.542997006\) \(a_{12}=+0.000000000\) \(a_{13}=+0.522348096\) \(a_{14}=+0.000000000\) \(a_{15}=+0.282565490\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.624211375\) \(a_{18}=+0.000000000\) \(a_{19}=-1.256906491\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.882174139\) \(a_{22}=+0.000000000\) \(a_{23}=-1.748281516\) \(a_{24}=+0.000000000\) \(a_{25}=-0.795489533\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.005717915\) \(a_{28}=+0.000000000\) \(a_{29}=-1.593846134\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.730551417\) \(a_{32}=+0.000000000\) \(a_{33}=-0.339280410\) \(a_{34}=+0.000000000\) \(a_{35}=-0.638485066\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.520469504\) \(a_{38}=+0.000000000\) \(a_{39}=-0.326378365\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.197310779\) \(a_{42}=+0.000000000\) \(a_{43}=-0.356414621\) \(a_{44}=+0.000000000\) \(a_{45}=+0.275673153\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.495962848\) \(a_{48}=+0.000000000\) \(a_{49}=+0.993360949\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.390025523\) \(a_{52}=+0.000000000\) \(a_{53}=+1.157119642\) \(a_{54}=+0.000000000\) \(a_{55}=-0.245558632\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.785351935\) \(a_{58}=+0.000000000\) \(a_{59}=-0.346778962\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.030022645\) \(a_{62}=+0.000000000\) \(a_{63}=-0.860656150\) \(a_{64}=+0.000000000\) \(a_{65}=-0.236220610\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.922260712\) \(a_{68}=+0.000000000\) \(a_{69}=+1.092377422\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.462404000\) \(a_{72}=+0.000000000\) \(a_{73}=-0.147210914\) \(a_{74}=+0.000000000\) \(a_{75}=+0.497045126\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.766638116\) \(a_{78}=+0.000000000\) \(a_{79}=-1.107400929\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.018813552\) \(a_{82}=+0.000000000\) \(a_{83}=-0.933481257\) \(a_{84}=+0.000000000\) \(a_{85}=-0.282286081\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.995881675\) \(a_{88}=+0.000000000\) \(a_{89}=-1.305701926\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.737484655\) \(a_{92}=+0.000000000\) \(a_{93}=+0.456469891\) \(a_{94}=+0.000000000\) \(a_{95}=+0.568408730\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.424080676\) \(a_{98}=+0.000000000\) \(a_{99}=-0.331004683\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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