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: \( 8.55288032905 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.465275928\) \(a_{4}=+0.000000000\) \(a_{5}=-1.214968102\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.251763833\) \(a_{8}=+0.000000000\) \(a_{9}=+1.147033546\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.266223088\) \(a_{12}=+0.000000000\) \(a_{13}=+1.263329217\) \(a_{14}=+0.000000000\) \(a_{15}=+1.780263513\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.221112140\) \(a_{18}=+0.000000000\) \(a_{19}=-0.996942359\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.834179413\) \(a_{22}=+0.000000000\) \(a_{23}=-0.534789197\) \(a_{24}=+0.000000000\) \(a_{25}=+0.476147488\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.215444716\) \(a_{28}=+0.000000000\) \(a_{29}=+0.553952388\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.598227898\) \(a_{32}=+0.000000000\) \(a_{33}=-0.390090298\) \(a_{34}=+0.000000000\) \(a_{35}=+1.520853145\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.724799755\) \(a_{38}=+0.000000000\) \(a_{39}=-1.851125891\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.076581833\) \(a_{42}=+0.000000000\) \(a_{43}=-0.043346157\) \(a_{44}=+0.000000000\) \(a_{45}=-1.393609170\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.798320301\) \(a_{48}=+0.000000000\) \(a_{49}=+0.566912695\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.323990296\) \(a_{52}=+0.000000000\) \(a_{53}=-0.261667914\) \(a_{54}=+0.000000000\) \(a_{55}=-0.323452560\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.460795640\) \(a_{58}=+0.000000000\) \(a_{59}=-0.358674887\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.269095302\) \(a_{62}=+0.000000000\) \(a_{63}=-1.435815110\) \(a_{64}=+0.000000000\) \(a_{65}=-1.534904700\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.282055123\) \(a_{68}=+0.000000000\) \(a_{69}=+0.783613737\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.139276357\) \(a_{72}=+0.000000000\) \(a_{73}=+0.606654438\) \(a_{74}=+0.000000000\) \(a_{75}=-0.697687408\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.333248498\) \(a_{78}=+0.000000000\) \(a_{79}=-0.155175529\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.831347591\) \(a_{82}=+0.000000000\) \(a_{83}=+0.614878396\) \(a_{84}=+0.000000000\) \(a_{85}=+0.268644197\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.811693100\) \(a_{88}=+0.000000000\) \(a_{89}=-0.350875727\) \(a_{90}=+0.000000000\)
\(a_{91}=-1.581389824\) \(a_{92}=+0.000000000\) \(a_{93}=+2.341844873\) \(a_{94}=+0.000000000\) \(a_{95}=+1.211253166\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.366372329\) \(a_{98}=+0.000000000\) \(a_{99}=+0.305366812\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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