Properties

Level $31$
Weight $0$
Character 31.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 4.02612573611 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.211216816\) \(a_{3}=-0.473033650\) \(a_{4}=-0.955387456\) \(a_{5}=+0.477277614\)
\(a_{6}=+0.099912662\) \(a_{7}=+0.625418722\) \(a_{8}=+0.413010714\) \(a_{9}=-0.776239166\) \(a_{10}=-0.100809058\)
\(a_{11}=+0.687074875\) \(a_{12}=+0.451930416\) \(a_{13}=+0.552028017\) \(a_{14}=-0.132098951\) \(a_{15}=-0.225768372\)
\(a_{16}=+0.868152648\) \(a_{17}=+1.898093699\) \(a_{18}=+0.163954765\) \(a_{19}=-0.806216474\) \(a_{20}=-0.455985046\)
\(a_{21}=-0.295844101\) \(a_{22}=-0.145121768\) \(a_{23}=+0.737258502\) \(a_{24}=-0.195367965\) \(a_{25}=-0.772206079\)
\(a_{26}=-0.116597600\) \(a_{27}=+0.840220896\) \(a_{28}=-0.597517202\) \(a_{29}=+0.198043106\) \(a_{30}=+0.047686077\)
\(a_{31}=-0.179605302\) \(a_{32}=-0.596379152\) \(a_{33}=-0.325009536\) \(a_{34}=-0.400909309\) \(a_{35}=+0.298498355\)
\(a_{36}=+0.741609162\) \(a_{37}=+1.151011123\) \(a_{38}=+0.170286477\) \(a_{39}=-0.261127828\) \(a_{40}=+0.197120768\)
\(a_{41}=+0.701794373\) \(a_{42}=+0.062487249\) \(a_{43}=+0.347063205\) \(a_{44}=-0.656422717\) \(a_{45}=-0.370481577\)
\(a_{46}=-0.155721394\) \(a_{47}=+1.380763497\) \(a_{48}=-0.410665416\) \(a_{49}=-0.608851423\) \(a_{50}=+0.163102910\)
\(a_{51}=-0.897862191\) \(a_{52}=-0.527400643\) \(a_{53}=+0.040783068\) \(a_{54}=-0.177468783\) \(a_{55}=+0.327925457\)
\(a_{56}=+0.258304632\) \(a_{57}=+0.381367521\) \(a_{58}=-0.041830035\) \(a_{59}=-0.633355766\) \(a_{60}=+0.215696271\)
\(a_{61}=-0.100023626\) \(a_{62}=+0.037935660\) \(a_{63}=-0.485474507\) \(a_{64}=-0.742187343\) \(a_{65}=+0.263470615\)
\(a_{66}=+0.068647479\) \(a_{67}=+1.472318352\) \(a_{68}=-1.813414911\) \(a_{69}=-0.348748081\) \(a_{70}=-0.063047874\)
\(a_{71}=-0.588830785\) \(a_{72}=-0.320595090\) \(a_{73}=+1.748319577\) \(a_{74}=-0.243112904\) \(a_{75}=+0.365279457\)
\(a_{76}=+0.770249101\) \(a_{77}=+0.429709490\) \(a_{78}=+0.055154597\) \(a_{79}=+0.259736299\) \(a_{80}=+0.414349813\)
\(a_{81}=+0.378786397\) \(a_{82}=-0.148230775\) \(a_{83}=+0.315101435\) \(a_{84}=+0.282645741\) \(a_{85}=+0.905917632\)
\(a_{86}=-0.073305592\) \(a_{87}=-0.093681044\) \(a_{88}=+0.283769303\) \(a_{89}=-1.448933061\) \(a_{90}=+0.078251918\)
\(a_{91}=+0.345248658\) \(a_{92}=-0.704367496\) \(a_{93}=+0.084959354\) \(a_{94}=-0.291640481\) \(a_{95}=-0.384789061\)
\(a_{96}=+0.282107351\) \(a_{97}=-1.161146829\) \(a_{98}=+0.128599754\) \(a_{99}=-0.533334358\) \(a_{100}=+0.737755923\)

Showing 100 of 1500 available coefficients

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