Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 26.6494958549 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.442998535\) \(a_{3}=-0.577350269\) \(a_{4}=+1.082244772\) \(a_{5}=+0.537024080\)
\(a_{6}=-0.833115593\) \(a_{7}=+0.211151534\) \(a_{8}=+0.118679086\) \(a_{9}=+0.333333333\) \(a_{10}=+0.774924960\)
\(a_{11}=-1.339573430\) \(a_{12}=-0.624834310\) \(a_{13}=-0.873131601\) \(a_{14}=+0.304691355\) \(a_{15}=-0.310050997\)
\(a_{16}=-0.910991025\) \(a_{17}=+0.804863922\) \(a_{18}=+0.480999512\) \(a_{19}=+1.665266579\) \(a_{20}=+0.581191503\)
\(a_{21}=-0.121908395\) \(a_{22}=-1.933002497\) \(a_{23}=-0.777447580\) \(a_{24}=-0.068519402\) \(a_{25}=-0.711605138\)
\(a_{26}=-1.259927620\) \(a_{27}=-0.192450090\) \(a_{28}=+0.228517644\) \(a_{29}=-0.633281483\) \(a_{30}=-0.447403134\)
\(a_{31}=-1.373398243\) \(a_{32}=-1.433237801\) \(a_{33}=+0.773403080\) \(a_{34}=+1.161417461\) \(a_{35}=+0.113393458\)
\(a_{36}=+0.360748257\) \(a_{37}=-1.832505667\) \(a_{38}=+2.402977235\) \(a_{39}=+0.504102765\) \(a_{40}=+0.063733527\)
\(a_{41}=+0.110858313\) \(a_{42}=-0.175913636\) \(a_{43}=-0.014525996\) \(a_{44}=-1.449746342\) \(a_{45}=+0.179008026\)
\(a_{46}=-1.121855719\) \(a_{47}=-0.752532980\) \(a_{48}=+0.525960914\) \(a_{49}=-0.955415029\) \(a_{50}=-1.026845172\)
\(a_{51}=-0.464688402\) \(a_{52}=-0.944942110\) \(a_{53}=-0.119675655\) \(a_{54}=-0.277705198\) \(a_{55}=-0.719383188\)
\(a_{56}=+0.025059271\) \(a_{57}=-0.961442108\) \(a_{58}=-0.913824252\) \(a_{59}=+1.647243264\) \(a_{60}=-0.335551070\)
\(a_{61}=+1.016252887\) \(a_{62}=-1.981811652\) \(a_{63}=+0.070383845\) \(a_{64}=-1.157169021\) \(a_{65}=-0.468892694\)
\(a_{66}=+1.116019512\) \(a_{67}=+0.080123354\) \(a_{68}=+0.871059772\) \(a_{69}=+0.448859570\) \(a_{70}=+0.163626594\)
\(a_{71}=-1.520837587\) \(a_{72}=+0.039559695\) \(a_{73}=+0.642887675\) \(a_{74}=-2.644302993\) \(a_{75}=+0.410845418\)
\(a_{76}=+1.802226050\) \(a_{77}=-0.282852985\) \(a_{78}=+0.727419551\) \(a_{79}=+0.386613580\) \(a_{80}=-0.489224117\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.159968383\) \(a_{83}=-1.548740080\) \(a_{84}=-0.131934723\) \(a_{85}=+0.432231307\)
\(a_{86}=-0.020960991\) \(a_{87}=+0.365625234\) \(a_{88}=-0.158979350\) \(a_{89}=+0.548506926\) \(a_{90}=+0.258308320\)
\(a_{91}=-0.184363077\) \(a_{92}=-0.841388579\) \(a_{93}=+0.792931845\) \(a_{94}=-1.085903987\) \(a_{95}=+0.894288252\)
\(a_{96}=+0.827480230\) \(a_{97}=+0.408713369\) \(a_{98}=-1.378662488\) \(a_{99}=-0.446524477\) \(a_{100}=-0.770130940\)

Showing 100 of 1228 available coefficients

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