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: \( 10.2048624763 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.537559954\)
\(a_{6}=+0.408248290\) \(a_{7}=+1.925651872\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.380112289\)
\(a_{11}=-0.341622323\) \(a_{12}=-0.288675135\) \(a_{13}=-1.293428114\) \(a_{14}=-1.361641497\) \(a_{15}=+0.310360384\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.875344408\) \(a_{18}=-0.235702260\) \(a_{19}=+0.294976684\) \(a_{20}=-0.268779977\)
\(a_{21}=-1.111775627\) \(a_{22}=+0.241563461\) \(a_{23}=+0.187162714\) \(a_{24}=+0.204124145\) \(a_{25}=-0.711029295\)
\(a_{26}=+0.914591791\) \(a_{27}=-0.192450090\) \(a_{28}=+0.962825936\) \(a_{29}=-0.976242075\) \(a_{30}=-0.219457933\)
\(a_{31}=-0.425532037\) \(a_{32}=-0.176776695\) \(a_{33}=+0.197235740\) \(a_{34}=+0.618961967\) \(a_{35}=-1.035153333\)
\(a_{36}=+0.166666667\) \(a_{37}=+1.226018268\) \(a_{38}=-0.208580014\) \(a_{39}=+0.746761070\) \(a_{40}=+0.190056145\)
\(a_{41}=-1.315826915\) \(a_{42}=+0.786144085\) \(a_{43}=-1.197323459\) \(a_{44}=-0.170811162\) \(a_{45}=-0.179186651\)
\(a_{46}=-0.132344024\) \(a_{47}=-0.746592811\) \(a_{48}=-0.144337567\) \(a_{49}=+2.708135134\) \(a_{50}=+0.502773636\)
\(a_{51}=+0.505380330\) \(a_{52}=-0.646714057\) \(a_{53}=-1.303588700\) \(a_{54}=+0.136082763\) \(a_{55}=+0.183642480\)
\(a_{56}=-0.680820749\) \(a_{57}=-0.170304868\) \(a_{58}=+0.690307391\) \(a_{59}=-0.054739154\) \(a_{60}=+0.155180192\)
\(a_{61}=-1.577875606\) \(a_{62}=+0.300896589\) \(a_{63}=+0.641883957\) \(a_{64}=+0.125000000\) \(a_{65}=+0.695295159\)
\(a_{66}=-0.139466730\) \(a_{67}=+0.067592383\) \(a_{68}=-0.437672203\) \(a_{69}=-0.108058446\) \(a_{70}=+0.731963940\)
\(a_{71}=+0.546756157\) \(a_{72}=-0.117851131\) \(a_{73}=-0.100907753\) \(a_{74}=-0.866925822\) \(a_{75}=+0.410512955\)
\(a_{76}=+0.147488342\) \(a_{77}=-0.657845666\) \(a_{78}=-0.528039816\) \(a_{79}=-0.374630055\) \(a_{80}=-0.134389989\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.930430134\) \(a_{83}=-0.650133914\) \(a_{84}=-0.555887813\) \(a_{85}=+0.470550100\)
\(a_{86}=+0.846635537\) \(a_{87}=+0.563633625\) \(a_{88}=+0.120781731\) \(a_{89}=+1.612084733\) \(a_{90}=+0.126704096\)
\(a_{91}=-2.490692270\) \(a_{92}=+0.093581357\) \(a_{93}=+0.245681036\) \(a_{94}=+0.527920840\) \(a_{95}=-0.158567653\)
\(a_{96}=+0.102062073\) \(a_{97}=+0.237414526\) \(a_{98}=-1.914940718\) \(a_{99}=-0.113874108\) \(a_{100}=-0.355514648\)

Showing 100 of 1000 available coefficients

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