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: \( 9.4700831342 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.560451032\) \(a_{4}=+0.000000000\) \(a_{5}=-1.335569158\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.083195544\) \(a_{8}=+0.000000000\) \(a_{9}=+1.435007422\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.910047298\) \(a_{12}=+0.000000000\) \(a_{13}=-0.590296445\) \(a_{14}=+0.000000000\) \(a_{15}=-2.084090271\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.508104855\) \(a_{18}=+0.000000000\) \(a_{19}=-0.848375543\) \(a_{20}=+0.000000000\)
\(a_{21}=-1.690273604\) \(a_{22}=+0.000000000\) \(a_{23}=-0.064217927\) \(a_{24}=+0.000000000\) \(a_{25}=+0.783744976\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.678807780\) \(a_{28}=+0.000000000\) \(a_{29}=-1.522309344\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.579866273\) \(a_{32}=+0.000000000\) \(a_{33}=-1.420084227\) \(a_{34}=+0.000000000\) \(a_{35}=+1.446682508\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.125348121\) \(a_{38}=+0.000000000\) \(a_{39}=-0.921128697\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.080207922\) \(a_{42}=+0.000000000\) \(a_{43}=+1.794034732\) \(a_{44}=+0.000000000\) \(a_{45}=-1.916551655\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.714370770\) \(a_{48}=+0.000000000\) \(a_{49}=+0.173312586\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.792872745\) \(a_{52}=+0.000000000\) \(a_{53}=+0.754316481\) \(a_{54}=+0.000000000\) \(a_{55}=+1.215431103\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.323848491\) \(a_{58}=+0.000000000\) \(a_{59}=+0.223477524\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.497461583\) \(a_{62}=+0.000000000\) \(a_{63}=-1.554393647\) \(a_{64}=+0.000000000\) \(a_{65}=+0.788381722\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.625396243\) \(a_{68}=+0.000000000\) \(a_{69}=-0.100208935\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.472144858\) \(a_{72}=+0.000000000\) \(a_{73}=-1.134264267\) \(a_{74}=+0.000000000\) \(a_{75}=+1.222995657\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.985759177\) \(a_{78}=+0.000000000\) \(a_{79}=+0.706610244\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.375761120\) \(a_{82}=+0.000000000\) \(a_{83}=-0.134280720\) \(a_{84}=+0.000000000\) \(a_{85}=-0.678609174\)
\(a_{86}=+0.000000000\) \(a_{87}=-2.375489188\) \(a_{88}=+0.000000000\) \(a_{89}=+0.077180902\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.639406478\) \(a_{92}=+0.000000000\) \(a_{93}=+0.904852933\) \(a_{94}=+0.000000000\) \(a_{95}=+1.133064211\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.565085156\) \(a_{98}=+0.000000000\) \(a_{99}=-1.305924627\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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