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: \( 12.5299513826 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.757886406\)
\(a_{6}=+0.408248290\) \(a_{7}=+0.478055798\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.535906617\)
\(a_{11}=+0.623872559\) \(a_{12}=-0.288675135\) \(a_{13}=+1.843610788\) \(a_{14}=-0.338036497\) \(a_{15}=+0.437565920\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.835309084\) \(a_{18}=-0.235702260\) \(a_{19}=-1.343772923\) \(a_{20}=-0.378943203\)
\(a_{21}=-0.276005644\) \(a_{22}=-0.441144517\) \(a_{23}=-0.427937138\) \(a_{24}=+0.204124145\) \(a_{25}=-0.425608196\)
\(a_{26}=-1.303629690\) \(a_{27}=-0.192450090\) \(a_{28}=+0.239027899\) \(a_{29}=-0.635627602\) \(a_{30}=-0.309405829\)
\(a_{31}=+1.270225503\) \(a_{32}=-0.176776693\) \(a_{33}=-0.360192942\) \(a_{34}=+0.590652717\) \(a_{35}=-0.362311991\)
\(a_{36}=+0.166666667\) \(a_{37}=-1.817984949\) \(a_{38}=+0.950190947\) \(a_{39}=-1.064409185\) \(a_{40}=+0.267953308\)
\(a_{41}=+0.633461146\) \(a_{42}=+0.195165462\) \(a_{43}=+1.082872216\) \(a_{44}=+0.311936280\) \(a_{45}=-0.252628802\)
\(a_{46}=+0.302597252\) \(a_{47}=-1.685885267\) \(a_{48}=-0.144337567\) \(a_{49}=-0.771462654\) \(a_{50}=+0.300950441\)
\(a_{51}=+0.482265924\) \(a_{52}=+0.921805394\) \(a_{53}=-0.472757199\) \(a_{54}=+0.136082764\) \(a_{55}=-0.472824532\)
\(a_{56}=-0.169018248\) \(a_{57}=+0.775827659\) \(a_{58}=+0.449456589\) \(a_{59}=-0.542972101\) \(a_{60}=+0.218782961\)
\(a_{61}=+0.738357574\) \(a_{62}=-0.898185075\) \(a_{63}=+0.159351933\) \(a_{64}=+0.125000002\) \(a_{65}=-1.397247553\)
\(a_{66}=+0.254694902\) \(a_{67}=+0.629785972\) \(a_{68}=-0.417654538\) \(a_{69}=+0.247069636\) \(a_{70}=+0.256193264\)
\(a_{71}=-1.523862325\) \(a_{72}=-0.117851141\) \(a_{73}=+1.113480633\) \(a_{74}=+1.285509539\) \(a_{75}=+0.245724924\)
\(a_{76}=-0.671886586\) \(a_{77}=+0.298245993\) \(a_{78}=+0.752650953\) \(a_{79}=-0.519351427\) \(a_{80}=-0.189471601\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.447924672\) \(a_{83}=-1.268406258\) \(a_{84}=-0.138002822\) \(a_{85}=+0.633069399\)
\(a_{86}=-0.765706287\) \(a_{87}=+0.366979768\) \(a_{88}=-0.220572259\) \(a_{89}=+0.011929713\) \(a_{90}=+0.178635539\)
\(a_{91}=+0.881348827\) \(a_{92}=-0.213968569\) \(a_{93}=-0.733365042\) \(a_{94}=+1.192100904\) \(a_{95}=+1.018427231\)
\(a_{96}=+0.102062073\) \(a_{97}=-0.563441585\) \(a_{98}=+0.545506475\) \(a_{99}=+0.207957519\) \(a_{100}=-0.212804098\)

Showing 100 of 1000 available coefficients

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