Properties

Level 10
Weight 0
Character 10.1
Symmetry even
Fricke sign +1

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: \(+1\)
Spectral parameter: \( 12.4596489912 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.853825302\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.603745661\) \(a_{7}=+1.789748957\) \(a_{8}=+0.353553391\) \(a_{9}=-0.270982354\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.409375907\) \(a_{12}=-0.426912651\) \(a_{13}=-0.452488940\) \(a_{14}=+1.265543624\) \(a_{15}=-0.381842283\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.430488888\) \(a_{18}=-0.191613460\) \(a_{19}=+0.053544293\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.528132944\) \(a_{22}=-0.996579261\) \(a_{23}=+1.534605562\) \(a_{24}=-0.301872830\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.319957998\) \(a_{27}=+1.085196892\) \(a_{28}=+0.894874479\) \(a_{29}=+0.127322681\) \(a_{30}=-0.270003268\)
\(a_{31}=-0.798448014\) \(a_{32}=+0.176776695\) \(a_{33}=+1.203360809\) \(a_{34}=+1.011508393\) \(a_{35}=+0.800400066\)
\(a_{36}=-0.135491177\) \(a_{37}=+1.839660898\) \(a_{38}=+0.037861532\) \(a_{39}=+0.386346506\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.230714311\) \(a_{42}=-1.080553167\) \(a_{43}=+0.421643251\) \(a_{44}=-0.704687953\) \(a_{45}=-0.121186993\)
\(a_{46}=+1.085129999\) \(a_{47}=+0.289060843\) \(a_{48}=-0.213456325\) \(a_{49}=+2.203201330\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.221387607\) \(a_{52}=-0.226244470\) \(a_{53}=-0.279495565\) \(a_{54}=+0.767350081\) \(a_{55}=-0.630292067\)
\(a_{56}=+0.632771812\) \(a_{57}=-0.045717472\) \(a_{58}=+0.090030731\) \(a_{59}=+0.740305330\) \(a_{60}=-0.190921142\)
\(a_{61}=-0.605669184\) \(a_{62}=-0.564588005\) \(a_{63}=-0.484990385\) \(a_{64}=+0.125000000\) \(a_{65}=-0.202359206\)
\(a_{66}=+0.850904588\) \(a_{67}=-0.273875602\) \(a_{68}=+0.715244444\) \(a_{69}=-1.310285057\) \(a_{70}=+0.565968315\)
\(a_{71}=+0.032239964\) \(a_{72}=-0.095806730\) \(a_{73}=+1.403221796\) \(a_{74}=+1.300836696\) \(a_{75}=-0.170765060\)
\(a_{76}=+0.026772146\) \(a_{77}=-2.522429060\) \(a_{78}=+0.273188234\) \(a_{79}=+0.585724301\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.655586209\) \(a_{82}=+0.163139654\) \(a_{83}=-0.291751204\) \(a_{84}=-0.764066472\) \(a_{85}=+0.639734079\)
\(a_{86}=+0.298146802\) \(a_{87}=-0.108711320\) \(a_{88}=-0.498289630\) \(a_{89}=+0.076704471\) \(a_{90}=-0.085692144\)
\(a_{91}=-0.809841601\) \(a_{92}=+0.767302781\) \(a_{93}=+0.681735143\) \(a_{94}=+0.204396882\) \(a_{95}=+0.023945736\)
\(a_{96}=-0.150936415\) \(a_{97}=+0.322174840\) \(a_{98}=+1.557898601\) \(a_{99}=+0.381916030\) \(a_{100}=+0.099975586\)

Showing 100 of 162 available coefficients

Rows: Cols: