Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 18.4077520222 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.903684982\) \(a_{3}=+0.577350269\) \(a_{4}=+2.624016512\) \(a_{5}=-0.803380448\)
\(a_{6}=-1.099093037\) \(a_{7}=-0.308944670\) \(a_{8}=-3.091615845\) \(a_{9}=+0.333333333\) \(a_{10}=+1.529383295\)
\(a_{11}=+0.501915062\) \(a_{12}=+1.514976640\) \(a_{13}=+0.385918340\) \(a_{14}=+0.588133329\) \(a_{15}=-0.463831918\)
\(a_{16}=+3.261446143\) \(a_{17}=-1.028368285\) \(a_{18}=-0.634561661\) \(a_{19}=+1.734674489\) \(a_{20}=-2.108083562\)
\(a_{21}=-0.178369288\) \(a_{22}=-0.955488167\) \(a_{23}=+0.342635030\) \(a_{24}=-1.784945240\) \(a_{25}=-0.354579855\)
\(a_{26}=-0.734666948\) \(a_{27}=+0.192450090\) \(a_{28}=-0.810675916\) \(a_{29}=+0.130931263\) \(a_{30}=+0.882989857\)
\(a_{31}=-0.084941017\) \(a_{32}=-3.117150199\) \(a_{33}=+0.289780796\) \(a_{34}=+1.957689260\) \(a_{35}=+0.248200108\)
\(a_{36}=+0.874672171\) \(a_{37}=-0.358124598\) \(a_{38}=-3.302273773\) \(a_{39}=+0.222810058\) \(a_{40}=+2.483743724\)
\(a_{41}=-0.613538521\) \(a_{42}=+0.339558936\) \(a_{43}=-0.866901895\) \(a_{44}=+1.317033412\) \(a_{45}=-0.267793483\)
\(a_{46}=-0.652269161\) \(a_{47}=-1.412188657\) \(a_{48}=+1.882996809\) \(a_{49}=-0.904553191\) \(a_{50}=+0.675008345\)
\(a_{51}=-0.593728706\) \(a_{52}=+1.012656097\) \(a_{53}=-0.561158065\) \(a_{54}=-0.366364346\) \(a_{55}=-0.403228748\)
\(a_{56}=+0.955138237\) \(a_{57}=+1.001514783\) \(a_{58}=-0.249251878\) \(a_{59}=-0.977498037\) \(a_{60}=-1.217102612\)
\(a_{61}=-0.080095700\) \(a_{62}=+0.161700939\) \(a_{63}=-0.102981557\) \(a_{64}=+2.672625878\) \(a_{65}=-0.310039249\)
\(a_{66}=-0.551651350\) \(a_{67}=+1.475018908\) \(a_{68}=-2.698455359\) \(a_{69}=+0.197820427\) \(a_{70}=-0.472494818\)
\(a_{71}=+1.424269942\) \(a_{72}=-1.030538615\) \(a_{73}=-1.685729222\) \(a_{74}=+0.681756420\) \(a_{75}=-0.204716775\)
\(a_{76}=+4.551814501\) \(a_{77}=-0.155063983\) \(a_{78}=-0.424160160\) \(a_{79}=-1.446111676\) \(a_{80}=-2.620182065\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.167984069\) \(a_{83}=-0.052432112\) \(a_{84}=-0.468043958\) \(a_{85}=+0.826170974\)
\(a_{86}=+1.650308119\) \(a_{87}=+0.075593200\) \(a_{88}=-1.551728560\) \(a_{89}=-1.170861753\) \(a_{90}=+0.509794432\)
\(a_{91}=-0.119227414\) \(a_{92}=+0.899079976\) \(a_{93}=-0.049040719\) \(a_{94}=+2.688362338\) \(a_{95}=-1.393603569\)
\(a_{96}=-1.799687506\) \(a_{97}=-0.959180852\) \(a_{98}=+1.721984325\) \(a_{99}=+0.167305021\) \(a_{100}=-0.930423394\)

Showing 100 of 1228 available coefficients

Rows: Cols: