Properties

Level $821$
Weight $0$
Character 821.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 821 \)
Weight: \( 0 \)
Character: 821.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 0.778754096529 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.896592223\) \(a_{3}=-0.316761987\) \(a_{4}=-0.196122226\) \(a_{5}=+0.064181829\)
\(a_{6}=+0.284006193\) \(a_{7}=-0.747923364\) \(a_{8}=+1.072433728\) \(a_{9}=-0.899661782\) \(a_{10}=-0.057544843\)
\(a_{11}=+0.549191629\) \(a_{12}=+0.062124191\) \(a_{13}=-0.165961894\) \(a_{14}=+0.670582256\) \(a_{15}=-0.020330388\)
\(a_{16}=-0.765413556\) \(a_{17}=-1.293574396\) \(a_{18}=+0.806629864\) \(a_{19}=-1.435987191\) \(a_{20}=-0.012587598\)
\(a_{21}=+0.236913702\) \(a_{22}=-0.492400908\) \(a_{23}=+0.336469857\) \(a_{24}=-0.339706284\) \(a_{25}=-0.995880629\)
\(a_{26}=+0.148800038\) \(a_{27}=+0.601740561\) \(a_{28}=+0.146684507\) \(a_{29}=+0.399822853\) \(a_{30}=+0.018228123\)
\(a_{31}=-1.127012026\) \(a_{32}=-0.386170002\) \(a_{33}=-0.173963030\) \(a_{34}=+1.159808879\) \(a_{35}=-0.048003118\)
\(a_{36}=+0.176443658\) \(a_{37}=+1.720313028\) \(a_{38}=+1.287494970\) \(a_{39}=+0.052570486\) \(a_{40}=+0.068830939\)
\(a_{41}=-0.185997061\) \(a_{42}=-0.212414947\) \(a_{43}=-0.932101957\) \(a_{44}=-0.107708890\) \(a_{45}=-0.057741891\)
\(a_{46}=-0.301676259\) \(a_{47}=+0.857374245\) \(a_{48}=+0.242454049\) \(a_{49}=-0.440610571\) \(a_{50}=+0.892898741\)
\(a_{51}=+0.409755129\) \(a_{52}=+0.032548784\) \(a_{53}=+0.076113898\) \(a_{54}=-0.539515859\) \(a_{55}=+0.035248167\)
\(a_{56}=-0.802098473\) \(a_{57}=+0.454866114\) \(a_{58}=-0.358478064\) \(a_{59}=-1.016009275\) \(a_{60}=+0.003987101\)
\(a_{61}=+0.879339694\) \(a_{62}=+1.010470241\) \(a_{63}=+0.672878046\) \(a_{64}=+1.111650870\) \(a_{65}=-0.010651702\)
\(a_{66}=+0.155973962\) \(a_{67}=-0.483383731\) \(a_{68}=+0.253698737\) \(a_{69}=-0.106580839\) \(a_{70}=+0.043039208\)
\(a_{71}=+1.734488148\) \(a_{72}=-0.964827794\) \(a_{73}=+0.174680489\) \(a_{74}=-1.542419417\) \(a_{75}=+0.315457197\)
\(a_{76}=+0.281628880\) \(a_{77}=-0.410753325\) \(a_{78}=-0.047134152\) \(a_{79}=-0.733775214\) \(a_{80}=-0.049125835\)
\(a_{81}=+0.709053232\) \(a_{82}=+0.166763606\) \(a_{83}=+0.882254440\) \(a_{84}=-0.046464013\) \(a_{85}=-0.083023960\)
\(a_{86}=+0.835715370\) \(a_{87}=-0.126648669\) \(a_{88}=+0.588972044\) \(a_{89}=-0.948215047\) \(a_{90}=+0.051771000\)
\(a_{91}=+0.124126735\) \(a_{92}=-0.065989033\) \(a_{93}=+0.356994548\) \(a_{94}=-0.768715118\) \(a_{95}=-0.092164126\)
\(a_{96}=+0.122323719\) \(a_{97}=+1.613318734\) \(a_{98}=+0.395048050\) \(a_{99}=-0.494086756\) \(a_{100}=+0.195314541\)

Showing 100 of 2350 available coefficients

Rows: Cols: