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: \( 5.27174063796 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.896705063\) \(a_{3}=+0.511519806\) \(a_{4}=-0.195920031\) \(a_{5}=+0.817526803\)
\(a_{6}=-0.458682400\) \(a_{7}=+0.167203959\) \(a_{8}=+1.072387546\) \(a_{9}=-0.738347488\) \(a_{10}=-0.733080423\)
\(a_{11}=-1.268849477\) \(a_{12}=-0.100216976\) \(a_{13}=+0.061871656\) \(a_{14}=-0.149932636\) \(a_{15}=+0.418181152\)
\(a_{16}=-0.765695311\) \(a_{17}=-1.441725261\) \(a_{18}=+0.662079931\) \(a_{19}=+0.229415734\) \(a_{20}=-0.160169876\)
\(a_{21}=+0.085528137\) \(a_{22}=+1.137783749\) \(a_{23}=-0.812340724\) \(a_{24}=+0.548547469\) \(a_{25}=-0.331649926\)
\(a_{26}=-0.055480627\) \(a_{27}=-0.889199170\) \(a_{28}=-0.032758605\) \(a_{29}=+0.929141360\) \(a_{30}=-0.374985156\)
\(a_{31}=-1.019874133\) \(a_{32}=-0.385784684\) \(a_{33}=-0.649041638\) \(a_{34}=+1.292802341\) \(a_{35}=+0.136693718\)
\(a_{36}=+0.144657062\) \(a_{37}=-0.654681861\) \(a_{38}=-0.205718250\) \(a_{39}=+0.031648578\) \(a_{40}=+0.876705562\)
\(a_{41}=+1.041705256\) \(a_{42}=-0.076693513\) \(a_{43}=+0.850387946\) \(a_{44}=+0.248593028\) \(a_{45}=-0.603618862\)
\(a_{46}=+0.728430040\) \(a_{47}=-0.854261874\) \(a_{48}=-0.391668317\) \(a_{49}=-0.972042836\) \(a_{50}=+0.297392168\)
\(a_{51}=-0.737471026\) \(a_{52}=-0.012121897\) \(a_{53}=-0.142640867\) \(a_{54}=+0.797349397\) \(a_{55}=-1.037318456\)
\(a_{56}=+0.179307443\) \(a_{57}=+0.117350692\) \(a_{58}=-0.833165762\) \(a_{59}=-0.267545164\) \(a_{60}=-0.081930064\)
\(a_{61}=-0.352660881\) \(a_{62}=+0.914526298\) \(a_{63}=-0.123454623\) \(a_{64}=+1.111630390\) \(a_{65}=+0.050581737\)
\(a_{66}=+0.581998923\) \(a_{67}=+1.193567442\) \(a_{68}=+0.282462857\) \(a_{69}=-0.415528370\) \(a_{70}=-0.122573949\)
\(a_{71}=+1.184155201\) \(a_{72}=-0.791794651\) \(a_{73}=-0.766594787\) \(a_{74}=+0.587056539\) \(a_{75}=-0.169645506\)
\(a_{76}=-0.044947138\) \(a_{77}=-0.212156656\) \(a_{78}=-0.028379440\) \(a_{79}=-1.052945739\) \(a_{80}=-0.625976440\)
\(a_{81}=+0.283504501\) \(a_{82}=-0.934102377\) \(a_{83}=+1.495435884\) \(a_{84}=-0.016756675\) \(a_{85}=-1.178649044\)
\(a_{86}=-0.762547177\) \(a_{87}=+0.475274208\) \(a_{88}=-1.360698376\) \(a_{89}=+1.795695597\) \(a_{90}=+0.541268089\)
\(a_{91}=+0.010345186\) \(a_{92}=+0.159153820\) \(a_{93}=-0.521685819\) \(a_{94}=+0.766020948\) \(a_{95}=+0.187553512\)
\(a_{96}=-0.197336507\) \(a_{97}=-1.344004986\) \(a_{98}=+0.871635732\) \(a_{99}=+0.936851824\) \(a_{100}=+0.064976864\)

Showing 100 of 546 available coefficients

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