Properties

Level $8$
Weight $0$
Character 8.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 4.64659164296 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.710698503\) \(a_{4}=+0.000000000\) \(a_{5}=-1.579704375\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.855778108\) \(a_{8}=+0.000000000\) \(a_{9}=-0.494907637\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.289301159\) \(a_{12}=+0.000000000\) \(a_{13}=-0.511880905\) \(a_{14}=+0.000000000\) \(a_{15}=+1.122693535\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.163156629\) \(a_{18}=+0.000000000\) \(a_{19}=-0.288341996\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.608200221\) \(a_{22}=+0.000000000\) \(a_{23}=-1.137795545\) \(a_{24}=+0.000000000\) \(a_{25}=+1.495465913\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.062428618\) \(a_{28}=+0.000000000\) \(a_{29}=-1.341783031\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.795862340\) \(a_{32}=+0.000000000\) \(a_{33}=+0.205605901\) \(a_{34}=+0.000000000\) \(a_{35}=-1.351876421\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.690427254\) \(a_{38}=+0.000000000\) \(a_{39}=+0.363792993\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.038808204\) \(a_{42}=+0.000000000\) \(a_{43}=+0.243278692\) \(a_{44}=+0.000000000\) \(a_{45}=+0.781807760\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.485599964\) \(a_{48}=+0.000000000\) \(a_{49}=-0.267643830\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.115955172\) \(a_{52}=+0.000000000\) \(a_{53}=-1.614862389\) \(a_{54}=+0.000000000\) \(a_{55}=+0.457010307\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.204924225\) \(a_{58}=+0.000000000\) \(a_{59}=+0.606794371\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.089728594\) \(a_{62}=+0.000000000\) \(a_{63}=-0.423531131\) \(a_{64}=+0.000000000\) \(a_{65}=+0.808620509\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.950295849\) \(a_{68}=+0.000000000\) \(a_{69}=+0.808629756\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.926464363\) \(a_{72}=+0.000000000\) \(a_{73}=-0.770461539\) \(a_{74}=+0.000000000\) \(a_{75}=-1.062825386\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.247577599\) \(a_{78}=+0.000000000\) \(a_{79}=+1.884595067\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.260158793\) \(a_{82}=+0.000000000\) \(a_{83}=-0.160713001\) \(a_{84}=+0.000000000\) \(a_{85}=-0.257739241\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.953603204\) \(a_{88}=+0.000000000\) \(a_{89}=+1.236550053\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.438056470\) \(a_{92}=+0.000000000\) \(a_{93}=-0.565618168\) \(a_{94}=+0.000000000\) \(a_{95}=+0.455495106\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.299402362\) \(a_{98}=+0.000000000\) \(a_{99}=+0.143177309\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

Rows: Cols: