Properties

Level $31$
Weight $0$
Character 31.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.6238542673 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.144769893\) \(a_{3}=+1.139319747\) \(a_{4}=+0.310498107\) \(a_{5}=-0.019514239\)
\(a_{6}=+1.304258945\) \(a_{7}=-0.176213601\) \(a_{8}=-0.789321008\) \(a_{9}=+0.298049487\) \(a_{10}=-0.022339313\)
\(a_{11}=+1.265211254\) \(a_{12}=+0.353756625\) \(a_{13}=+0.460693987\) \(a_{14}=-0.201724026\) \(a_{15}=-0.022232958\)
\(a_{16}=-1.214089032\) \(a_{17}=+0.817380003\) \(a_{18}=+0.341198079\) \(a_{19}=-1.026603462\) \(a_{20}=-0.006059134\)
\(a_{21}=-0.200763636\) \(a_{22}=+1.448375751\) \(a_{23}=-0.714836186\) \(a_{24}=-0.899289012\) \(a_{25}=-0.999619194\)
\(a_{26}=+0.527388606\) \(a_{27}=-0.799746081\) \(a_{28}=-0.054713990\) \(a_{29}=+1.388014612\) \(a_{30}=-0.025451621\)
\(a_{31}=-0.179605302\) \(a_{32}=-0.600531563\) \(a_{33}=+1.441480166\) \(a_{34}=+0.935712018\) \(a_{35}=+0.003438674\)
\(a_{36}=+0.092543801\) \(a_{37}=+1.080288351\) \(a_{38}=-1.175224734\) \(a_{39}=+0.524877757\) \(a_{40}=+0.015402999\)
\(a_{41}=-0.709985774\) \(a_{42}=-0.229828166\) \(a_{43}=+1.619916872\) \(a_{44}=+0.392845699\) \(a_{45}=-0.005816209\)
\(a_{46}=-0.818322944\) \(a_{47}=-0.228636067\) \(a_{48}=-1.383235610\) \(a_{49}=-0.968948767\) \(a_{50}=-1.144333958\)
\(a_{51}=+0.931257178\) \(a_{52}=+0.143044611\) \(a_{53}=-1.027893353\) \(a_{54}=-0.915525236\) \(a_{55}=-0.024689635\)
\(a_{56}=+0.139089098\) \(a_{57}=-1.169629597\) \(a_{58}=+1.588957339\) \(a_{59}=-0.001901143\) \(a_{60}=-0.006903291\)
\(a_{61}=+1.565497842\) \(a_{62}=-0.205606742\) \(a_{63}=-0.052520373\) \(a_{64}=+0.526618580\) \(a_{65}=-0.008990093\)
\(a_{66}=+1.650163094\) \(a_{67}=+1.378117886\) \(a_{68}=+0.253794943\) \(a_{69}=-0.814426983\) \(a_{70}=+0.003936491\)
\(a_{71}=+0.458373205\) \(a_{72}=-0.235256721\) \(a_{73}=-1.066985496\) \(a_{74}=+1.236681579\) \(a_{75}=-1.138885888\)
\(a_{76}=-0.318758431\) \(a_{77}=-0.222947432\) \(a_{78}=+0.600864254\) \(a_{79}=-1.142561325\) \(a_{80}=+0.023692024\)
\(a_{81}=-1.209215990\) \(a_{82}=-0.812770338\) \(a_{83}=+0.881783065\) \(a_{84}=-0.062336729\) \(a_{85}=-0.015950549\)
\(a_{86}=+1.854432063\) \(a_{87}=+1.581392458\) \(a_{88}=-0.998657822\) \(a_{89}=-1.215231542\) \(a_{90}=-0.006658221\)
\(a_{91}=-0.081180547\) \(a_{92}=-0.221955282\) \(a_{93}=-0.204627867\) \(a_{94}=-0.261735686\) \(a_{95}=+0.020033385\)
\(a_{96}=-0.684197469\) \(a_{97}=+1.514054917\) \(a_{98}=-1.109223376\) \(a_{99}=+0.377095565\) \(a_{100}=-0.310379867\)

Showing 100 of 546 available coefficients

Rows: Cols: