Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 20.0135298126 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.266246527\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.895371506\) \(a_{7}=+0.643628021\) \(a_{8}=+0.353553391\) \(a_{9}=+0.603380266\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.052594454\) \(a_{12}=-0.633123263\) \(a_{13}=-1.232480167\) \(a_{14}=+0.455113738\) \(a_{15}=+0.566282662\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.220281208\) \(a_{18}=+0.426654278\) \(a_{19}=+1.192467279\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.814991746\) \(a_{22}=-0.037189895\) \(a_{23}=-0.718154695\) \(a_{24}=-0.447685753\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.871495084\) \(a_{27}=+0.502218360\) \(a_{28}=+0.321814011\) \(a_{29}=+1.734991444\) \(a_{30}=+0.400422310\)
\(a_{31}=+1.028693144\) \(a_{32}=+0.176776695\) \(a_{33}=+0.066597544\) \(a_{34}=+0.155762336\) \(a_{35}=-0.287839201\)
\(a_{36}=+0.301690133\) \(a_{37}=-0.492524815\) \(a_{38}=+0.843201699\) \(a_{39}=+1.560623731\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.352560719\) \(a_{42}=-0.576286190\) \(a_{43}=-1.202788319\) \(a_{44}=-0.026297227\) \(a_{45}=-0.269839858\)
\(a_{46}=-0.507812055\) \(a_{47}=+0.544795189\) \(a_{48}=-0.316561632\) \(a_{49}=-0.585742970\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.278930314\) \(a_{52}=-0.616240083\) \(a_{53}=-1.863883140\) \(a_{54}=+0.355122008\) \(a_{55}=+0.023520955\)
\(a_{56}=+0.227556869\) \(a_{57}=-1.509957550\) \(a_{58}=+1.226824216\) \(a_{59}=-0.218943802\) \(a_{60}=+0.283141331\)
\(a_{61}=-0.385591329\) \(a_{62}=+0.727395898\) \(a_{63}=+0.388352447\) \(a_{64}=+0.125000000\) \(a_{65}=+0.551181887\)
\(a_{66}=+0.047091575\) \(a_{67}=+1.653525257\) \(a_{68}=+0.110140604\) \(a_{69}=+0.909360888\) \(a_{70}=-0.203533051\)
\(a_{71}=-1.814571533\) \(a_{72}=+0.213327139\) \(a_{73}=-0.850179045\) \(a_{74}=-0.348267636\) \(a_{75}=-0.253249305\)
\(a_{76}=+0.596233640\) \(a_{77}=-0.033851264\) \(a_{78}=+1.103527623\) \(a_{79}=-0.332004545\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.239312521\) \(a_{82}=+0.249298075\) \(a_{83}=+0.581366851\) \(a_{84}=-0.407495873\) \(a_{85}=-0.098512751\)
\(a_{86}=-0.850499777\) \(a_{87}=-2.196926890\) \(a_{88}=-0.018594947\) \(a_{89}=-0.400178802\) \(a_{90}=-0.190805594\)
\(a_{91}=-0.793258771\) \(a_{92}=-0.359077348\) \(a_{93}=-1.302579120\) \(a_{94}=+0.385228373\) \(a_{95}=-0.533287579\)
\(a_{96}=-0.223842876\) \(a_{97}=+1.096106212\) \(a_{98}=-0.414182826\) \(a_{99}=-0.031734455\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

Rows: Cols: