Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 11.5585635397 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.205942514\)
\(a_{6}=-0.408248290\) \(a_{7}=+0.724519233\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.852730130\)
\(a_{11}=+0.830052303\) \(a_{12}=-0.288675135\) \(a_{13}=-0.415742779\) \(a_{14}=+0.512312463\) \(a_{15}=+0.696251235\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.803208888\) \(a_{18}=+0.235702260\) \(a_{19}=+0.744141729\) \(a_{20}=-0.602971257\)
\(a_{21}=-0.418301374\) \(a_{22}=+0.586935612\) \(a_{23}=+1.885243349\) \(a_{24}=-0.204124145\) \(a_{25}=+0.454297348\)
\(a_{26}=-0.293974538\) \(a_{27}=-0.192450090\) \(a_{28}=+0.362259617\) \(a_{29}=-1.594581394\) \(a_{30}=+0.492323970\)
\(a_{31}=+0.907246030\) \(a_{32}=+0.176776699\) \(a_{33}=-0.479230920\) \(a_{34}=+1.275061232\) \(a_{35}=-0.873728546\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.548426035\) \(a_{38}=+0.526187663\) \(a_{39}=+0.240029205\) \(a_{40}=-0.426365065\)
\(a_{41}=+0.041023313\) \(a_{42}=-0.295783738\) \(a_{43}=-0.946974992\) \(a_{44}=+0.415026151\) \(a_{45}=-0.401980838\)
\(a_{46}=+1.333068356\) \(a_{47}=+0.920011286\) \(a_{48}=-0.144337567\) \(a_{49}=-0.475071880\) \(a_{50}=+0.321236735\)
\(a_{51}=-1.041083137\) \(a_{52}=-0.207871389\) \(a_{53}=+1.177334176\) \(a_{54}=-0.136082763\) \(a_{55}=-1.000995361\)
\(a_{56}=+0.256156232\) \(a_{57}=-0.429630428\) \(a_{58}=-1.127539317\) \(a_{59}=+0.440306046\) \(a_{60}=+0.348125618\)
\(a_{61}=+0.866582909\) \(a_{62}=+0.641519820\) \(a_{63}=+0.241506411\) \(a_{64}=+0.125000000\) \(a_{65}=+0.501361892\)
\(a_{66}=-0.338867434\) \(a_{67}=-0.813466919\) \(a_{68}=+0.901604444\) \(a_{69}=-1.088445755\) \(a_{70}=-0.617819379\)
\(a_{71}=-0.654303562\) \(a_{72}=+0.117851129\) \(a_{73}=+0.460464656\) \(a_{74}=-0.387795772\) \(a_{75}=-0.262288694\)
\(a_{76}=+0.372070863\) \(a_{77}=+0.601388856\) \(a_{78}=+0.169726279\) \(a_{79}=+0.842707628\) \(a_{80}=-0.301485629\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.029007863\) \(a_{83}=+1.393734158\) \(a_{84}=-0.209150687\) \(a_{85}=-2.174566260\)
\(a_{86}=-0.669612438\) \(a_{87}=+0.920631997\) \(a_{88}=+0.293467806\) \(a_{89}=-0.177345895\) \(a_{90}=-0.284243377\)
\(a_{91}=-0.301213639\) \(a_{92}=+0.942621674\) \(a_{93}=-0.523798740\) \(a_{94}=+0.650546219\) \(a_{95}=-0.897392148\)
\(a_{96}=-0.102062073\) \(a_{97}=-0.517085927\) \(a_{98}=-0.335926548\) \(a_{99}=+0.276684101\) \(a_{100}=+0.227148674\)

Showing 100 of 1000 available coefficients

Rows: Cols: