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: \( 31.4813463946 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.525618137\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.078774930\) \(a_{7}=-0.347132466\) \(a_{8}=-0.353553391\) \(a_{9}=+1.327510700\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.648486797\) \(a_{12}=+0.762809068\) \(a_{13}=+0.855339127\) \(a_{14}=+0.245459721\) \(a_{15}=+0.682277172\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.867528303\) \(a_{18}=-0.938691818\) \(a_{19}=-0.763519403\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.529591586\) \(a_{22}=-1.165656193\) \(a_{23}=-1.158669092\) \(a_{24}=-0.539387465\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.604816097\) \(a_{27}=+0.499656264\) \(a_{28}=-0.173566233\) \(a_{29}=-1.206075067\) \(a_{30}=-0.482442815\)
\(a_{31}=-1.082194431\) \(a_{32}=-0.176776695\) \(a_{33}=+2.514961357\) \(a_{34}=+0.613435146\) \(a_{35}=-0.155242358\)
\(a_{36}=+0.663755350\) \(a_{37}=-1.561124522\) \(a_{38}=+0.539889747\) \(a_{39}=+1.304920886\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.695727825\) \(a_{42}=+0.374477802\) \(a_{43}=-0.659762280\) \(a_{44}=+0.824243399\) \(a_{45}=+0.593680833\)
\(a_{46}=+0.819302772\) \(a_{47}=-0.601635668\) \(a_{48}=+0.381404534\) \(a_{49}=-0.879499051\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.323516913\) \(a_{52}=+0.427669564\) \(a_{53}=-1.349016128\) \(a_{54}=-0.353310332\) \(a_{55}=+0.737225708\)
\(a_{56}=+0.122729860\) \(a_{57}=-1.164839049\) \(a_{58}=+0.852823859\) \(a_{59}=+0.270348702\) \(a_{60}=+0.341138586\)
\(a_{61}=+0.920306296\) \(a_{62}=+0.765227021\) \(a_{63}=-0.460822063\) \(a_{64}=+0.125000000\) \(a_{65}=+0.382519287\)
\(a_{66}=-1.778346230\) \(a_{67}=+0.709571536\) \(a_{68}=-0.433764151\) \(a_{69}=-1.767686581\) \(a_{70}=+0.109772924\)
\(a_{71}=-1.401285382\) \(a_{72}=-0.469345909\) \(a_{73}=+0.081230150\) \(a_{74}=+1.103881736\) \(a_{75}=+0.305123627\)
\(a_{76}=-0.381759701\) \(a_{77}=-0.572243287\) \(a_{78}=-0.922718407\) \(a_{79}=-1.684486730\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.565226041\) \(a_{82}=-0.491953863\) \(a_{83}=+1.227741815\) \(a_{84}=-0.264795793\) \(a_{85}=-0.387970451\)
\(a_{86}=+0.466522382\) \(a_{87}=-1.840009997\) \(a_{88}=-0.582828097\) \(a_{89}=-1.225879090\) \(a_{90}=-0.419795743\)
\(a_{91}=-0.296915981\) \(a_{92}=-0.579334546\) \(a_{93}=-1.651015452\) \(a_{94}=+0.425420660\) \(a_{95}=-0.341456257\)
\(a_{96}=-0.269693733\) \(a_{97}=+0.634259294\) \(a_{98}=+0.621899743\) \(a_{99}=+2.188383862\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

Rows: Cols: