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: \( 0.9600460427 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.812213658\) \(a_{3}=-1.603157633\) \(a_{4}=-0.340309684\) \(a_{5}=+0.789361605\)
\(a_{6}=+1.302106678\) \(a_{7}=+0.774997587\) \(a_{8}=+1.088618075\) \(a_{9}=+1.570113273\) \(a_{10}=-0.641130055\)
\(a_{11}=+1.797468958\) \(a_{12}=+0.545570755\) \(a_{13}=+0.480118533\) \(a_{14}=-0.629462985\) \(a_{15}=-1.265470611\)
\(a_{16}=-0.543880760\) \(a_{17}=-0.309465710\) \(a_{18}=-1.275267195\) \(a_{19}=+1.321840717\) \(a_{20}=-0.268627790\)
\(a_{21}=-1.242442846\) \(a_{22}=-1.459928914\) \(a_{23}=-0.490956702\) \(a_{24}=-1.745225061\) \(a_{25}=-0.376909715\)
\(a_{26}=-0.389957743\) \(a_{27}=-0.913979768\) \(a_{28}=-0.263738961\) \(a_{29}=-0.516813042\) \(a_{30}=+1.027831936\)
\(a_{31}=+1.379165860\) \(a_{32}=-0.646871279\) \(a_{33}=-2.881624778\) \(a_{34}=+0.251352443\) \(a_{35}=+0.611752995\)
\(a_{36}=-0.534324686\) \(a_{37}=+0.326478763\) \(a_{38}=-1.073616399\) \(a_{39}=-0.769704530\) \(a_{40}=+0.859313042\)
\(a_{41}=+1.126778528\) \(a_{42}=+1.009128131\) \(a_{43}=+0.446690410\) \(a_{44}=-0.611695679\) \(a_{45}=+1.239386878\)
\(a_{46}=+0.398761513\) \(a_{47}=-0.286646880\) \(a_{48}=+0.871925590\) \(a_{49}=-0.399380422\) \(a_{50}=+0.306130816\)
\(a_{51}=+0.496122399\) \(a_{52}=-0.163388467\) \(a_{53}=-0.229134082\) \(a_{54}=+0.742346650\) \(a_{55}=+1.418852104\)
\(a_{56}=+0.843675498\) \(a_{57}=-2.119118284\) \(a_{58}=+0.419761794\) \(a_{59}=-1.070194781\) \(a_{60}=+0.430651763\)
\(a_{61}=+0.485951334\) \(a_{62}=-1.120177121\) \(a_{63}=+1.216832766\) \(a_{64}=+1.069276934\) \(a_{65}=+0.378986715\)
\(a_{66}=+2.340494735\) \(a_{67}=+1.376934616\) \(a_{68}=+0.105314894\) \(a_{69}=+0.787080972\) \(a_{70}=-0.496874130\)
\(a_{71}=-0.311237134\) \(a_{72}=+1.709252141\) \(a_{73}=-0.063042136\) \(a_{74}=-0.265170567\) \(a_{75}=+0.604243880\)
\(a_{76}=-0.449835892\) \(a_{77}=+1.393033341\) \(a_{78}=+0.625163740\) \(a_{79}=+0.930052881\) \(a_{80}=-0.429318682\)
\(a_{81}=-0.104860493\) \(a_{82}=-0.915184519\) \(a_{83}=-1.096888966\) \(a_{84}=+0.422815355\) \(a_{85}=-0.244280845\)
\(a_{86}=-0.362807970\) \(a_{87}=+0.828531706\) \(a_{88}=+1.956755989\) \(a_{89}=-1.373149327\) \(a_{90}=-1.006646458\)
\(a_{91}=+0.372089717\) \(a_{92}=+0.167077625\) \(a_{93}=-2.211019696\) \(a_{94}=+0.232818198\) \(a_{95}=+1.043410125\)
\(a_{96}=+1.037036287\) \(a_{97}=+0.844766706\) \(a_{98}=+0.324381638\) \(a_{99}=+2.822228081\) \(a_{100}=+0.128265758\)

Showing 100 of 2410 available coefficients

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