Properties

Level $19$
Weight $0$
Character 19.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 4.27865718529 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.578584600\) \(a_{3}=+0.774250986\) \(a_{4}=+1.491929339\) \(a_{5}=+0.772814394\)
\(a_{6}=+1.222220684\) \(a_{7}=-0.480816109\) \(a_{8}=+0.776552079\) \(a_{9}=-0.400535410\) \(a_{10}=+1.219952901\)
\(a_{11}=-0.208237359\) \(a_{12}=+1.155127762\) \(a_{13}=+1.008758321\) \(a_{14}=-0.759008905\) \(a_{15}=+0.598352307\)
\(a_{16}=-0.266076186\) \(a_{17}=-1.744828388\) \(a_{18}=-0.632279030\) \(a_{19}=-0.229415734\) \(a_{20}=+1.152984468\)
\(a_{21}=-0.372272347\) \(a_{22}=-0.328720289\) \(a_{23}=+1.477669249\) \(a_{24}=+0.601246213\) \(a_{25}=-0.402757912\)
\(a_{26}=+1.592410350\) \(a_{27}=-1.084365923\) \(a_{28}=-0.717343660\) \(a_{29}=+1.321417331\) \(a_{30}=+0.944549737\)
\(a_{31}=-0.059222479\) \(a_{32}=-1.196575849\) \(a_{33}=-0.161227981\) \(a_{34}=-2.754359223\) \(a_{35}=-0.371581610\)
\(a_{36}=-0.597570530\) \(a_{37}=+1.258105901\) \(a_{38}=-0.362152144\) \(a_{39}=+0.781032125\) \(a_{40}=+0.600130625\)
\(a_{41}=+1.328155946\) \(a_{42}=-0.587663394\) \(a_{43}=-0.127846028\) \(a_{44}=-0.310675426\) \(a_{45}=-0.309539530\)
\(a_{46}=+2.332625920\) \(a_{47}=+0.225341907\) \(a_{48}=-0.206009749\) \(a_{49}=-0.768815869\) \(a_{50}=-0.635787438\)
\(a_{51}=-1.350935100\) \(a_{52}=+1.504996135\) \(a_{53}=+0.033239539\) \(a_{54}=-1.711763346\) \(a_{55}=-0.160928829\)
\(a_{56}=-0.373378749\) \(a_{57}=-0.177625358\) \(a_{58}=+2.085969050\) \(a_{59}=+0.658924065\) \(a_{60}=+0.892699362\)
\(a_{61}=+0.249279126\) \(a_{62}=-0.093487694\) \(a_{63}=+0.192583878\) \(a_{64}=-1.622820022\) \(a_{65}=+0.779582950\)
\(a_{66}=-0.254512008\) \(a_{67}=-0.173934081\) \(a_{68}=-2.603160664\) \(a_{69}=+1.144086873\) \(a_{70}=-0.586573007\)
\(a_{71}=-0.866349438\) \(a_{72}=-0.311036606\) \(a_{73}=-1.369749575\) \(a_{74}=+1.986026601\) \(a_{75}=-0.311835711\)
\(a_{76}=-0.342272064\) \(a_{77}=+0.100123877\) \(a_{78}=+1.232925284\) \(a_{79}=+1.885582058\) \(a_{80}=-0.205627506\)
\(a_{81}=-0.439035975\) \(a_{82}=+2.096606522\) \(a_{83}=+0.205525013\) \(a_{84}=-0.555404036\) \(a_{85}=-1.348428494\)
\(a_{86}=-0.201815771\) \(a_{87}=+1.023108672\) \(a_{88}=-0.161707154\) \(a_{89}=-0.641999512\) \(a_{90}=-0.488634336\)
\(a_{91}=-0.485027251\) \(a_{92}=+2.204578106\) \(a_{93}=-0.045853063\) \(a_{94}=+0.355721264\) \(a_{95}=-0.177295781\)
\(a_{96}=-0.926450031\) \(a_{97}=+1.779688989\) \(a_{98}=-1.213640891\) \(a_{99}=+0.083406436\) \(a_{100}=-0.600886346\)

Showing 100 of 546 available coefficients

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