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: \( 11.8777730802 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.620621677\) \(a_{4}=+0.000000000\) \(a_{5}=-1.665947265\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.365394976\) \(a_{8}=+0.000000000\) \(a_{9}=+1.626414620\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.726352902\) \(a_{12}=+0.000000000\) \(a_{13}=+0.987647467\) \(a_{14}=+0.000000000\) \(a_{15}=-2.699870250\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.084186844\) \(a_{18}=+0.000000000\) \(a_{19}=+0.391839878\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.592167019\) \(a_{22}=+0.000000000\) \(a_{23}=+0.318277390\) \(a_{24}=+0.000000000\) \(a_{25}=+1.775380289\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.015181113\) \(a_{28}=+0.000000000\) \(a_{29}=+0.758834490\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.206609885\) \(a_{32}=+0.000000000\) \(a_{33}=+1.177143259\) \(a_{34}=+0.000000000\) \(a_{35}=-0.608728761\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.890145879\) \(a_{38}=+0.000000000\) \(a_{39}=+1.600602901\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.537079104\) \(a_{42}=+0.000000000\) \(a_{43}=-0.189532881\) \(a_{44}=+0.000000000\) \(a_{45}=-2.709520988\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.030791591\) \(a_{48}=+0.000000000\) \(a_{49}=-0.866486511\) \(a_{50}=+0.000000000\)
\(a_{51}=+1.757056701\) \(a_{52}=+0.000000000\) \(a_{53}=+0.287753714\) \(a_{54}=+0.000000000\) \(a_{55}=-1.210065631\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.635024201\) \(a_{58}=+0.000000000\) \(a_{59}=+1.060311415\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.389969445\) \(a_{62}=+0.000000000\) \(a_{63}=+0.594283731\) \(a_{64}=+0.000000000\) \(a_{65}=-1.645368596\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.750422479\) \(a_{68}=+0.000000000\) \(a_{69}=+0.515807237\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.549138637\) \(a_{72}=+0.000000000\) \(a_{73}=+0.611039166\) \(a_{74}=+0.000000000\) \(a_{75}=+2.877219780\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.265405701\) \(a_{78}=+0.000000000\) \(a_{79}=-1.874613465\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.018809888\) \(a_{82}=+0.000000000\) \(a_{83}=-0.969808434\) \(a_{84}=+0.000000000\) \(a_{85}=-1.806198081\)
\(a_{86}=+0.000000000\) \(a_{87}=+1.229783576\) \(a_{88}=+0.000000000\) \(a_{89}=+1.447166415\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.360881423\) \(a_{92}=+0.000000000\) \(a_{93}=-0.334836459\) \(a_{94}=+0.000000000\) \(a_{95}=-0.652784574\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.570209746\) \(a_{98}=+0.000000000\) \(a_{99}=+1.181350980\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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