Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 19.4234814708 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.692761976\) \(a_{3}=+1.562354302\) \(a_{4}=-0.520080844\) \(a_{5}=-0.038411698\)
\(a_{6}=-1.082339654\) \(a_{7}=+0.312952981\) \(a_{8}=+1.053054210\) \(a_{9}=+1.440950965\) \(a_{10}=+0.026610165\)
\(a_{11}=+1.153633548\) \(a_{12}=-0.812550466\) \(a_{13}=+0.758971426\) \(a_{14}=-0.216801925\) \(a_{15}=-0.060012682\)
\(a_{16}=-0.209435072\) \(a_{17}=+0.844381010\) \(a_{18}=-0.998236039\) \(a_{19}=+0.393212897\) \(a_{20}=+0.019977188\)
\(a_{21}=+0.488943436\) \(a_{22}=-0.799193461\) \(a_{23}=-0.357998743\) \(a_{24}=+1.645243775\) \(a_{25}=-0.998524541\)
\(a_{26}=-0.525786545\) \(a_{27}=+0.688921638\) \(a_{28}=-0.162760850\) \(a_{29}=+0.224703572\) \(a_{30}=+0.041574504\)
\(a_{31}=-0.330286117\) \(a_{32}=-0.907965556\) \(a_{33}=+1.802384347\) \(a_{34}=-0.584955057\) \(a_{35}=-0.012021055\)
\(a_{36}=-0.749410994\) \(a_{37}=+0.403965398\) \(a_{38}=-0.272402944\) \(a_{39}=+1.185782272\) \(a_{40}=-0.040449601\)
\(a_{41}=-1.379815225\) \(a_{42}=-0.338721421\) \(a_{43}=+1.644724472\) \(a_{44}=-0.599982713\) \(a_{45}=-0.055349374\)
\(a_{46}=+0.248007917\) \(a_{47}=-0.018395947\) \(a_{48}=-0.327211786\) \(a_{49}=-0.902060431\) \(a_{50}=+0.691739836\)
\(a_{51}=+1.319222301\) \(a_{52}=-0.394726497\) \(a_{53}=-0.666756117\) \(a_{54}=-0.477258722\) \(a_{55}=-0.044313019\)
\(a_{56}=+0.329556456\) \(a_{57}=+0.614337860\) \(a_{58}=-0.155666109\) \(a_{59}=+0.321647370\) \(a_{60}=+0.031211446\)
\(a_{61}=-1.493591904\) \(a_{62}=+0.228809663\) \(a_{63}=+0.450949900\) \(a_{64}=+0.838439084\) \(a_{65}=-0.029153381\)
\(a_{66}=-1.248623342\) \(a_{67}=+1.413320337\) \(a_{68}=-0.439146388\) \(a_{69}=-0.559320876\) \(a_{70}=+0.008327730\)
\(a_{71}=-1.308408222\) \(a_{72}=+1.517399480\) \(a_{73}=+1.527966975\) \(a_{74}=-0.279851867\) \(a_{75}=-1.560049113\)
\(a_{76}=-0.204502495\) \(a_{77}=+0.361033060\) \(a_{78}=-0.821464870\) \(a_{79}=+1.269723424\) \(a_{80}=+0.008044757\)
\(a_{81}=-0.364611280\) \(a_{82}=+0.955883522\) \(a_{83}=-0.513767608\) \(a_{84}=-0.254290115\) \(a_{85}=-0.032434108\)
\(a_{86}=-1.139402576\) \(a_{87}=+0.351066590\) \(a_{88}=+1.214838673\) \(a_{89}=-0.359149084\) \(a_{90}=+0.038343939\)
\(a_{91}=+0.237522371\) \(a_{92}=+0.186188285\) \(a_{93}=-0.516023930\) \(a_{94}=+0.012744012\) \(a_{95}=-0.015103986\)
\(a_{96}=-1.418563879\) \(a_{97}=+0.335176901\) \(a_{98}=+0.624913182\) \(a_{99}=+1.662329394\) \(a_{100}=+0.519313427\)

Showing 100 of 5000 available coefficients

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