Properties

Level $6$
Weight $0$
Character 6.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 12.1162222939 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.496668805\)
\(a_{6}=-0.408248290\) \(a_{7}=+1.419907600\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-1.058304661\)
\(a_{11}=-0.582997000\) \(a_{12}=+0.288675135\) \(a_{13}=-0.966651745\) \(a_{14}=-1.004026293\) \(a_{15}=+0.864102137\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.575903872\) \(a_{18}=-0.235702260\) \(a_{19}=+0.412639744\) \(a_{20}=+0.748334402\)
\(a_{21}=+0.819784035\) \(a_{22}=+0.412241132\) \(a_{23}=-0.461786265\) \(a_{24}=-0.204124145\) \(a_{25}=+1.240017511\)
\(a_{26}=+0.683526004\) \(a_{27}=+0.192450089\) \(a_{28}=+0.709953801\) \(a_{29}=-1.211257581\) \(a_{30}=-0.611012489\)
\(a_{31}=+0.907247320\) \(a_{32}=-0.176776671\) \(a_{33}=-0.336593564\) \(a_{34}=-1.114332314\) \(a_{35}=+2.125131410\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.773663796\) \(a_{38}=-0.291780361\) \(a_{39}=-0.558096645\) \(a_{40}=-0.529152330\)
\(a_{41}=-0.391827044\) \(a_{42}=-0.579674850\) \(a_{43}=+0.545554485\) \(a_{44}=-0.291498500\) \(a_{45}=+0.498889602\)
\(a_{46}=+0.326532200\) \(a_{47}=-0.189246090\) \(a_{48}=+0.144337567\) \(a_{49}=+1.016137593\) \(a_{50}=-0.876824791\)
\(a_{51}=+0.909848525\) \(a_{52}=-0.483325873\) \(a_{53}=-0.081608404\) \(a_{54}=-0.136082763\) \(a_{55}=-0.872553423\)
\(a_{56}=-0.502013146\) \(a_{57}=+0.238237667\) \(a_{58}=+0.856488450\) \(a_{59}=-1.219045005\) \(a_{60}=+0.432051068\)
\(a_{61}=+1.394440579\) \(a_{62}=-0.641520727\) \(a_{63}=+0.473302534\) \(a_{64}=+0.124999999\) \(a_{65}=-1.446757514\)
\(a_{66}=+0.238007532\) \(a_{67}=+1.457131639\) \(a_{68}=+0.787951926\) \(a_{69}=-0.266612420\) \(a_{70}=-1.502694817\)
\(a_{71}=-0.251912407\) \(a_{72}=-0.117851148\) \(a_{73}=+0.349222524\) \(a_{74}=-0.547062862\) \(a_{75}=+0.715924383\)
\(a_{76}=+0.206319794\) \(a_{77}=-0.827801871\) \(a_{78}=+0.394633922\) \(a_{79}=-1.428547287\) \(a_{80}=+0.374167201\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.277063560\) \(a_{83}=+0.944846320\) \(a_{84}=+0.409892018\) \(a_{85}=+2.358606164\)
\(a_{86}=-0.385765276\) \(a_{87}=-0.699319891\) \(a_{88}=+0.206120566\) \(a_{89}=-1.694184993\) \(a_{90}=-0.352768220\)
\(a_{91}=-1.372556160\) \(a_{92}=-0.230893133\) \(a_{93}=+0.523799481\) \(a_{94}=+0.133817194\) \(a_{95}=+0.617585032\)
\(a_{96}=-0.102062072\) \(a_{97}=+0.115417685\) \(a_{98}=-0.718517783\) \(a_{99}=-0.194332334\) \(a_{100}=+0.620008755\)

Showing 100 of 1000 available coefficients

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