Properties

Level $61$
Weight $0$
Character 61.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 61 \)
Weight: \( 0 \)
Character: 61.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.67704450723 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.760555477\) \(a_{3}=+0.459990764\) \(a_{4}=+2.099555587\) \(a_{5}=-0.872463508\)
\(a_{6}=-0.809839259\) \(a_{7}=-0.832302224\) \(a_{8}=-1.935828610\) \(a_{9}=-0.788408497\) \(a_{10}=+1.536020407\)
\(a_{11}=+0.036204603\) \(a_{12}=+0.965776179\) \(a_{13}=+1.303688257\) \(a_{14}=+1.465314239\) \(a_{15}=-0.401325156\)
\(a_{16}=+1.308578074\) \(a_{17}=-0.318683034\) \(a_{18}=+1.388036897\) \(a_{19}=+0.725501658\) \(a_{20}=-1.831785632\)
\(a_{21}=-0.382851336\) \(a_{22}=-0.063740212\) \(a_{23}=+1.037220789\) \(a_{24}=-0.890463282\) \(a_{25}=-0.238807428\)
\(a_{26}=-2.295215501\) \(a_{27}=-0.822651391\) \(a_{28}=-1.747464785\) \(a_{29}=+0.957535979\) \(a_{30}=+0.706555201\)
\(a_{31}=-0.966452460\) \(a_{32}=-0.367995686\) \(a_{33}=+0.016653783\) \(a_{34}=+0.561059160\) \(a_{35}=+0.726153318\)
\(a_{36}=-1.655307464\) \(a_{37}=+1.501433006\) \(a_{38}=-1.277285917\) \(a_{39}=+0.599684558\) \(a_{40}=+1.688939819\)
\(a_{41}=+0.727771682\) \(a_{42}=+0.674031017\) \(a_{43}=-1.516481729\) \(a_{44}=+0.076013577\) \(a_{45}=+0.687857643\)
\(a_{46}=-1.826084740\) \(a_{47}=-1.004275704\) \(a_{48}=+0.601933829\) \(a_{49}=-0.307273008\) \(a_{50}=+0.420433724\)
\(a_{51}=-0.146591252\) \(a_{52}=+2.737165964\) \(a_{53}=+0.415496300\) \(a_{54}=+1.448323412\) \(a_{55}=-0.031587195\)
\(a_{56}=+1.611194458\) \(a_{57}=+0.333724062\) \(a_{58}=-1.685795211\) \(a_{59}=-0.433324414\) \(a_{60}=-0.842604473\)
\(a_{61}=-0.128036880\) \(a_{62}=+1.701493172\) \(a_{63}=+0.656194145\) \(a_{64}=-0.660701254\) \(a_{65}=-1.137420430\)
\(a_{66}=-0.029319909\) \(a_{67}=-1.097371207\) \(a_{68}=-0.669092744\) \(a_{69}=+0.477111983\) \(a_{70}=-1.278433201\)
\(a_{71}=-0.524524338\) \(a_{72}=+1.526223724\) \(a_{73}=+0.414772351\) \(a_{74}=-2.643356102\) \(a_{75}=-0.109849211\)
\(a_{76}=+1.523231059\) \(a_{77}=-0.030133172\) \(a_{78}=-1.055777933\) \(a_{79}=+1.573781822\) \(a_{80}=-1.141686617\)
\(a_{81}=+0.409996455\) \(a_{82}=-1.281282421\) \(a_{83}=+0.296630309\) \(a_{84}=-0.803817662\) \(a_{85}=+0.278039318\)
\(a_{86}=+2.669850212\) \(a_{87}=+0.440457707\) \(a_{88}=-0.070085907\) \(a_{89}=-0.398319135\) \(a_{90}=-1.211011540\)
\(a_{91}=-1.085062636\) \(a_{92}=+2.177702701\) \(a_{93}=-0.444559206\) \(a_{94}=+1.768083091\) \(a_{95}=-0.632973722\)
\(a_{96}=-0.169274617\) \(a_{97}=+1.504520666\) \(a_{98}=+0.540971176\) \(a_{99}=-0.028544017\) \(a_{100}=-0.501389469\)

Showing 100 of 546 available coefficients

Rows: Cols: