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: \( 11.7819543736 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.530598839\) \(a_{4}=+0.000000000\) \(a_{5}=+1.547641308\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.142314206\) \(a_{8}=+0.000000000\) \(a_{9}=-0.718464872\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.066405533\) \(a_{12}=+0.000000000\) \(a_{13}=-0.985910182\) \(a_{14}=+0.000000000\) \(a_{15}=-0.821176681\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.522466413\) \(a_{18}=+0.000000000\) \(a_{19}=+1.619981905\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.075511753\) \(a_{22}=+0.000000000\) \(a_{23}=+0.701921113\) \(a_{24}=+0.000000000\) \(a_{25}=+1.395193617\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.911815466\) \(a_{28}=+0.000000000\) \(a_{29}=+1.365123368\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.106674757\) \(a_{32}=+0.000000000\) \(a_{33}=-0.565833538\) \(a_{34}=+0.000000000\) \(a_{35}=-0.220251344\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.690906441\) \(a_{38}=+0.000000000\) \(a_{39}=+0.523122799\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.420695521\) \(a_{42}=+0.000000000\) \(a_{43}=+1.625056127\) \(a_{44}=+0.000000000\) \(a_{45}=-1.111925914\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.101764591\) \(a_{48}=+0.000000000\) \(a_{49}=-0.979746667\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.277220072\) \(a_{52}=+0.000000000\) \(a_{53}=+0.637803236\) \(a_{54}=+0.000000000\) \(a_{55}=+1.650413254\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.859560518\) \(a_{58}=+0.000000000\) \(a_{59}=-0.532986903\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.020175082\) \(a_{62}=+0.000000000\) \(a_{63}=+0.102247758\) \(a_{64}=+0.000000000\) \(a_{65}=-1.525835324\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.655373758\) \(a_{68}=+0.000000000\) \(a_{69}=-0.372438528\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.120716534\) \(a_{72}=+0.000000000\) \(a_{73}=+1.239284745\) \(a_{74}=+0.000000000\) \(a_{75}=-0.740288113\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.151764658\) \(a_{78}=+0.000000000\) \(a_{79}=-0.424083364\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.234656643\) \(a_{82}=+0.000000000\) \(a_{83}=+0.252897370\) \(a_{84}=+0.000000000\) \(a_{85}=-0.808590588\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.724332890\) \(a_{88}=+0.000000000\) \(a_{89}=-0.224582123\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.140309025\) \(a_{92}=+0.000000000\) \(a_{93}=+0.056601502\) \(a_{94}=+0.000000000\) \(a_{95}=+2.507150913\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.198591908\) \(a_{98}=+0.000000000\) \(a_{99}=-0.766174915\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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