Properties

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

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Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 9.01322849206 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.371240192\) \(a_{4}=+0.000000000\) \(a_{5}=-0.079238077\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.502221739\) \(a_{8}=+0.000000000\) \(a_{9}=-0.862180720\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.262680878\) \(a_{12}=+0.000000000\) \(a_{13}=+1.651356980\) \(a_{14}=+0.000000000\) \(a_{15}=+0.029416359\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.688730299\) \(a_{18}=+0.000000000\) \(a_{19}=+1.228081624\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.186444895\) \(a_{22}=+0.000000000\) \(a_{23}=+0.179389832\) \(a_{24}=+0.000000000\) \(a_{25}=-0.993721327\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.691316328\) \(a_{28}=+0.000000000\) \(a_{29}=-0.622220113\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.720635615\) \(a_{32}=+0.000000000\) \(a_{33}=-0.468757892\) \(a_{34}=+0.000000000\) \(a_{35}=+0.039795085\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.958277002\) \(a_{38}=+0.000000000\) \(a_{39}=-0.613050083\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.689257233\) \(a_{42}=+0.000000000\) \(a_{43}=+0.361571558\) \(a_{44}=+0.000000000\) \(a_{45}=+0.068317542\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.120064262\) \(a_{48}=+0.000000000\) \(a_{49}=-0.747773325\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.255684369\) \(a_{52}=+0.000000000\) \(a_{53}=-0.394295828\) \(a_{54}=+0.000000000\) \(a_{55}=-0.100052405\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.455913258\) \(a_{58}=+0.000000000\) \(a_{59}=-0.726139199\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.692063883\) \(a_{62}=+0.000000000\) \(a_{63}=+0.433005900\) \(a_{64}=+0.000000000\) \(a_{65}=-0.130850351\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.602395077\) \(a_{68}=+0.000000000\) \(a_{69}=-0.066596716\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.885179578\) \(a_{72}=+0.000000000\) \(a_{73}=-0.963482357\) \(a_{74}=+0.000000000\) \(a_{75}=+0.368909297\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.634145786\) \(a_{78}=+0.000000000\) \(a_{79}=+0.224752387\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.605536314\) \(a_{82}=+0.000000000\) \(a_{83}=+0.294344132\) \(a_{84}=+0.000000000\) \(a_{85}=-0.054573664\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.230993114\) \(a_{88}=+0.000000000\) \(a_{89}=+1.554341938\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.829347373\) \(a_{92}=+0.000000000\) \(a_{93}=-0.638769097\) \(a_{94}=+0.000000000\) \(a_{95}=-0.097310826\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.151396285\) \(a_{98}=+0.000000000\) \(a_{99}=-1.088659108\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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