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: \( 6.58769285315 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.266147507\) \(a_{4}=+0.000000000\) \(a_{5}=-0.198194989\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.744223028\) \(a_{8}=+0.000000000\) \(a_{9}=-0.929165504\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.691748235\) \(a_{12}=+0.000000000\) \(a_{13}=-1.200589816\) \(a_{14}=+0.000000000\) \(a_{15}=-0.052749102\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.391667448\) \(a_{18}=+0.000000000\) \(a_{19}=+1.313596304\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.464220611\) \(a_{22}=+0.000000000\) \(a_{23}=+0.121704717\) \(a_{24}=+0.000000000\) \(a_{25}=-0.960718746\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.513442590\) \(a_{28}=+0.000000000\) \(a_{29}=+1.158654344\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.298731488\) \(a_{32}=+0.000000000\) \(a_{33}=+0.184107069\) \(a_{34}=+0.000000000\) \(a_{35}=+0.345696263\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.155362711\) \(a_{38}=+0.000000000\) \(a_{39}=-0.319533987\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.302173550\) \(a_{42}=+0.000000000\) \(a_{43}=+0.517649189\) \(a_{44}=+0.000000000\) \(a_{45}=+0.184155947\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.345343304\) \(a_{48}=+0.000000000\) \(a_{49}=+2.042313971\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.104241315\) \(a_{52}=+0.000000000\) \(a_{53}=-1.620367406\) \(a_{54}=+0.000000000\) \(a_{55}=-0.137101034\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.349610382\) \(a_{58}=+0.000000000\) \(a_{59}=-0.929344403\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.830989856\) \(a_{62}=+0.000000000\) \(a_{63}=+1.620671869\) \(a_{64}=+0.000000000\) \(a_{65}=+0.237950885\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.596096826\) \(a_{68}=+0.000000000\) \(a_{69}=+0.032391407\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.572455854\) \(a_{72}=+0.000000000\) \(a_{73}=+1.051951160\) \(a_{74}=+0.000000000\) \(a_{75}=-0.255692896\)
\(a_{76}=+0.000000000\) \(a_{77}=-1.206563201\) \(a_{78}=+0.000000000\) \(a_{79}=-1.138551462\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.792514039\) \(a_{82}=+0.000000000\) \(a_{83}=-0.356914433\) \(a_{84}=+0.000000000\) \(a_{85}=+0.077626525\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.308372965\) \(a_{88}=+0.000000000\) \(a_{89}=-0.274844016\) \(a_{90}=+0.000000000\)
\(a_{91}=+2.094096405\) \(a_{92}=+0.000000000\) \(a_{93}=+0.079506641\) \(a_{94}=+0.000000000\) \(a_{95}=-0.260348204\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.014587629\) \(a_{98}=+0.000000000\) \(a_{99}=-0.642748598\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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