Properties

Level $31$
Weight $0$
Character 31.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.96542621139 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.597927172\) \(a_{3}=-0.462788238\) \(a_{4}=+1.553371246\) \(a_{5}=+0.268757832\)
\(a_{6}=-0.739501900\) \(a_{7}=-0.915464602\) \(a_{8}=+0.884246950\) \(a_{9}=-0.785827047\) \(a_{10}=+0.429455443\)
\(a_{11}=+1.441325446\) \(a_{12}=-0.718881942\) \(a_{13}=+0.971843077\) \(a_{14}=-1.462845762\) \(a_{15}=-0.124377964\)
\(a_{16}=-0.140409019\) \(a_{17}=-0.719428221\) \(a_{18}=-1.255694391\) \(a_{19}=+1.765692771\) \(a_{20}=+0.417480689\)
\(a_{21}=+0.423666250\) \(a_{22}=+2.303133094\) \(a_{23}=-0.291506957\) \(a_{24}=-0.409219088\) \(a_{25}=-0.927769228\)
\(a_{26}=+1.552934459\) \(a_{27}=+0.826459752\) \(a_{28}=-1.422056389\) \(a_{29}=-0.855086823\) \(a_{30}=-0.198746928\)
\(a_{31}=+0.179605302\) \(a_{32}=-1.108610335\) \(a_{33}=-0.667028463\) \(a_{34}=-1.149593902\) \(a_{35}=-0.246038282\)
\(a_{36}=-1.220681139\) \(a_{37}=-0.785431019\) \(a_{38}=+2.821448455\) \(a_{39}=-0.449757545\) \(a_{40}=+0.237648293\)
\(a_{41}=+0.411862062\) \(a_{42}=+0.676987813\) \(a_{43}=+0.028276839\) \(a_{44}=+2.238913504\) \(a_{45}=-0.211197174\)
\(a_{46}=-0.465806887\) \(a_{47}=-0.048203350\) \(a_{48}=+0.064979642\) \(a_{49}=-0.161924562\) \(a_{50}=-1.482507658\)
\(a_{51}=+0.332942919\) \(a_{52}=+1.509633091\) \(a_{53}=+1.381202415\) \(a_{54}=+1.320622494\) \(a_{55}=+0.387367502\)
\(a_{56}=-0.809496782\) \(a_{57}=-0.817141846\) \(a_{58}=-1.366366468\) \(a_{59}=-1.715696648\) \(a_{60}=-0.193205152\)
\(a_{61}=+1.141168611\) \(a_{62}=+0.286996192\) \(a_{63}=+0.719396845\) \(a_{64}=-1.631069559\) \(a_{65}=+0.261190439\)
\(a_{66}=-1.065862906\) \(a_{67}=+0.708428703\) \(a_{68}=-1.117539112\) \(a_{69}=+0.134905991\) \(a_{70}=-0.393151256\)
\(a_{71}=-0.128652545\) \(a_{72}=-0.694865169\) \(a_{73}=+0.262205990\) \(a_{74}=-1.255061567\) \(a_{75}=+0.429360686\)
\(a_{76}=+2.742776379\) \(a_{77}=-1.319482426\) \(a_{78}=-0.718679802\) \(a_{79}=+1.528935981\) \(a_{80}=-0.037736023\)
\(a_{81}=+0.403351195\) \(a_{82}=+0.658125581\) \(a_{83}=+0.150072360\) \(a_{84}=+0.658110971\) \(a_{85}=-0.193351969\)
\(a_{86}=+0.045184329\) \(a_{87}=+0.395724124\) \(a_{88}=+1.274487629\) \(a_{89}=-0.361921848\) \(a_{90}=-0.337477702\)
\(a_{91}=-0.889687935\) \(a_{92}=-0.452818525\) \(a_{93}=-0.083119221\) \(a_{94}=-0.077025443\) \(a_{95}=+0.474543761\)
\(a_{96}=+0.513051824\) \(a_{97}=-1.309829620\) \(a_{98}=-0.258743658\) \(a_{99}=-1.132632519\) \(a_{100}=-1.441170041\)

Showing 100 of 546 available coefficients

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