Properties

Level $991$
Weight $0$
Character 991.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 991 \)
Weight: \( 0 \)
Character: 991.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.46548074405 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.444551638\) \(a_{3}=+0.152657776\) \(a_{4}=+1.086729264\) \(a_{5}=+0.757852831\)
\(a_{6}=-0.220522111\) \(a_{7}=-0.816664761\) \(a_{8}=-0.125284657\) \(a_{9}=-0.976695780\) \(a_{10}=-1.094757441\)
\(a_{11}=+1.193688382\) \(a_{12}=+0.165897701\) \(a_{13}=-0.898928036\) \(a_{14}=+1.179714301\) \(a_{15}=+0.115692127\)
\(a_{16}=-0.905748991\) \(a_{17}=+1.570366561\) \(a_{18}=+1.410887401\) \(a_{19}=+0.214572141\) \(a_{20}=+0.823580555\)
\(a_{21}=-0.124670374\) \(a_{22}=-1.724344219\) \(a_{23}=-1.721488333\) \(a_{24}=-0.019125742\) \(a_{25}=-0.425659375\)
\(a_{26}=+1.298548150\) \(a_{27}=-0.301757808\) \(a_{28}=-0.887493445\) \(a_{29}=-0.648349736\) \(a_{30}=-0.167123189\)
\(a_{31}=-0.946046351\) \(a_{32}=+1.433685911\) \(a_{33}=+0.182225827\) \(a_{34}=-2.268475543\) \(a_{35}=-0.618911747\)
\(a_{36}=-1.061403638\) \(a_{37}=+0.620383182\) \(a_{38}=-0.309960667\) \(a_{39}=-0.137228273\) \(a_{40}=-0.094947117\)
\(a_{41}=+1.255627294\) \(a_{42}=+0.180092604\) \(a_{43}=+0.841102235\) \(a_{44}=+1.297215969\) \(a_{45}=-0.740191553\)
\(a_{46}=+2.486778451\) \(a_{47}=-0.954663339\) \(a_{48}=-0.138269579\) \(a_{49}=-0.333058883\) \(a_{50}=+0.614886935\)
\(a_{51}=+0.239728855\) \(a_{52}=-0.976891530\) \(a_{53}=+1.432589996\) \(a_{54}=+0.435905032\) \(a_{55}=+0.904640156\)
\(a_{56}=+0.102315609\) \(a_{57}=+0.032756130\) \(a_{58}=+0.936574622\) \(a_{59}=-1.082709954\) \(a_{60}=+0.125726001\)
\(a_{61}=-1.305964834\) \(a_{62}=+1.366613016\) \(a_{63}=+0.797633123\) \(a_{64}=-1.165284132\) \(a_{65}=-0.681254892\)
\(a_{66}=-0.263234656\) \(a_{67}=-0.794403499\) \(a_{68}=+1.706563271\) \(a_{69}=-0.262798430\) \(a_{70}=+0.894049715\)
\(a_{71}=-0.578673088\) \(a_{72}=+0.122364988\) \(a_{73}=+0.773727625\) \(a_{74}=-0.896175464\) \(a_{75}=-0.064980197\)
\(a_{76}=+0.233181919\) \(a_{77}=-0.974843065\) \(a_{78}=+0.198233608\) \(a_{79}=-0.456065732\) \(a_{80}=-0.686424519\)
\(a_{81}=+0.930629927\) \(a_{82}=-1.813818310\) \(a_{83}=-0.518190741\) \(a_{84}=-0.135482752\) \(a_{85}=+1.190106559\)
\(a_{86}=-1.215015584\) \(a_{87}=-0.098975821\) \(a_{88}=-0.149551050\) \(a_{89}=-1.957397782\) \(a_{90}=+1.069244845\)
\(a_{91}=+0.734123261\) \(a_{92}=-1.870791387\) \(a_{93}=-0.144421442\) \(a_{94}=+1.379060314\) \(a_{95}=+0.162614053\)
\(a_{96}=+0.218863226\) \(a_{97}=-0.934738534\) \(a_{98}=+0.481120643\) \(a_{99}=-1.165870064\) \(a_{100}=-0.462576511\)

Showing 100 of 2620 available coefficients

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