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: \( 24.2298934341 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.761445972\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.245530391\) \(a_{7}=+0.116152925\) \(a_{8}=-0.353553391\) \(a_{9}=+2.102691912\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.333466473\) \(a_{12}=-0.880722986\) \(a_{13}=+1.167726318\) \(a_{14}=-0.082132521\) \(a_{15}=+0.787742586\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.412230981\) \(a_{18}=-1.486827710\) \(a_{19}=+1.876472734\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.204597101\) \(a_{22}=+0.942903185\) \(a_{23}=+1.592568118\) \(a_{24}=+0.622765196\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.825707198\) \(a_{27}=-1.942332227\) \(a_{28}=+0.058076462\) \(a_{29}=+0.510299232\) \(a_{30}=-0.557018125\)
\(a_{31}=+1.142835827\) \(a_{32}=-0.176776695\) \(a_{33}=+2.348829147\) \(a_{34}=-0.291491322\) \(a_{35}=-0.051945167\)
\(a_{36}=+1.051345956\) \(a_{37}=+1.372621163\) \(a_{38}=-1.326866595\) \(a_{39}=-2.056886819\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.027130182\) \(a_{42}=+0.144671998\) \(a_{43}=-0.099340496\) \(a_{44}=-0.666733236\) \(a_{45}=-0.940352410\)
\(a_{46}=-1.126115716\) \(a_{47}=-0.781566605\) \(a_{48}=-0.440361493\) \(a_{49}=-0.986508498\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.726122601\) \(a_{52}=+0.583863159\) \(a_{53}=+0.229220830\) \(a_{54}=+1.373436289\) \(a_{55}=+0.596344336\)
\(a_{56}=-0.041066260\) \(a_{57}=-3.305305339\) \(a_{58}=-0.360836048\) \(a_{59}=+0.111313381\) \(a_{60}=+0.393871293\)
\(a_{61}=+1.346761564\) \(a_{62}=-0.808106963\) \(a_{63}=+0.244233815\) \(a_{64}=+0.125000000\) \(a_{65}=-0.522223085\)
\(a_{66}=-1.660873018\) \(a_{67}=-0.045547133\) \(a_{68}=+0.206115490\) \(a_{69}=-2.805222696\) \(a_{70}=+0.036730780\)
\(a_{71}=+0.309262553\) \(a_{72}=-0.743413855\) \(a_{73}=+0.385446573\) \(a_{74}=-0.970589732\) \(a_{75}=-0.352289194\)
\(a_{76}=+0.938236367\) \(a_{77}=-0.154886031\) \(a_{78}=+1.454438617\) \(a_{79}=-1.268839811\) \(a_{80}=-0.111803399\)
\(a_{81}=+1.318621366\) \(a_{82}=-0.019183936\) \(a_{83}=+0.727659643\) \(a_{84}=-0.102298551\) \(a_{85}=-0.184355299\)
\(a_{86}=+0.070244338\) \(a_{87}=-0.898864527\) \(a_{88}=+0.471451593\) \(a_{89}=-1.093775745\) \(a_{90}=+0.664929566\)
\(a_{91}=+0.135634827\) \(a_{92}=+0.796284059\) \(a_{93}=-2.013043565\) \(a_{94}=+0.552651046\) \(a_{95}=-0.839184118\)
\(a_{96}=+0.311382598\) \(a_{97}=+0.995830186\) \(a_{98}=+0.697566849\) \(a_{99}=-2.803869167\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

Rows: Cols: