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: \( 30.8102571845 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.933375803\) \(a_{3}=+0.577350269\) \(a_{4}=+2.737941997\) \(a_{5}=+0.865681264\)
\(a_{6}=+1.116235041\) \(a_{7}=+0.423527995\) \(a_{8}=+3.360095005\) \(a_{9}=+0.333333333\) \(a_{10}=+1.673687210\)
\(a_{11}=+0.727381842\) \(a_{12}=+1.580751549\) \(a_{13}=-1.498143545\) \(a_{14}=+0.818838777\) \(a_{15}=+0.499801311\)
\(a_{16}=+3.758384383\) \(a_{17}=+0.592884468\) \(a_{18}=+0.644458601\) \(a_{19}=-0.632628932\) \(a_{20}=+2.370185090\)
\(a_{21}=+0.244524002\) \(a_{22}=+1.406302453\) \(a_{23}=-0.774124047\) \(a_{24}=+1.939951756\) \(a_{25}=-0.250595949\)
\(a_{26}=-2.896474481\) \(a_{27}=+0.192450090\) \(a_{28}=+1.159595084\) \(a_{29}=-1.417131144\) \(a_{30}=+0.966303761\)
\(a_{31}=+0.298296355\) \(a_{32}=+3.906274421\) \(a_{33}=+0.419954102\) \(a_{34}=+1.146268484\) \(a_{35}=+0.366640250\)
\(a_{36}=+0.912647332\) \(a_{37}=+1.253468217\) \(a_{38}=-1.223109469\) \(a_{39}=-0.864953579\) \(a_{40}=+2.908771292\)
\(a_{41}=-0.560716765\) \(a_{42}=+0.472756788\) \(a_{43}=-0.244598131\) \(a_{44}=+1.991529293\) \(a_{45}=+0.288560421\)
\(a_{46}=-1.496672702\) \(a_{47}=-0.319586233\) \(a_{48}=+2.169904235\) \(a_{49}=-0.820624038\) \(a_{50}=-0.484496144\)
\(a_{51}=+0.342302007\) \(a_{52}=-4.101830131\) \(a_{53}=+0.681805527\) \(a_{54}=+0.372078347\) \(a_{55}=+0.629680833\)
\(a_{56}=+1.423094300\) \(a_{57}=-0.365248484\) \(a_{58}=-2.739847065\) \(a_{59}=+0.992130741\) \(a_{60}=+1.368427000\)
\(a_{61}=-0.213384620\) \(a_{62}=+0.576718954\) \(a_{63}=+0.141175998\) \(a_{64}=+3.793912065\) \(a_{65}=-1.296914798\)
\(a_{66}=+0.811929100\) \(a_{67}=-0.490970616\) \(a_{68}=+1.623283284\) \(a_{69}=-0.446940727\) \(a_{70}=+0.708853388\)
\(a_{71}=-0.395209076\) \(a_{72}=+1.120031668\) \(a_{73}=+0.825433873\) \(a_{74}=+2.423425122\) \(a_{75}=-0.144681638\)
\(a_{76}=-1.732101321\) \(a_{77}=+0.308066573\) \(a_{78}=-1.672280321\) \(a_{79}=+0.911984004\) \(a_{80}=+3.253562945\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.084076226\) \(a_{83}=-1.437674485\) \(a_{84}=+0.669492534\) \(a_{85}=+0.513248976\)
\(a_{86}=-0.472900109\) \(a_{87}=-0.818181048\) \(a_{88}=+2.444072094\) \(a_{89}=+0.322485446\) \(a_{90}=+0.557895737\)
\(a_{91}=-0.634505732\) \(a_{92}=-2.119506740\) \(a_{93}=+0.172221481\) \(a_{94}=-0.617880290\) \(a_{95}=-0.547655013\)
\(a_{96}=+2.255288589\) \(a_{97}=+1.358562616\) \(a_{98}=-1.586574658\) \(a_{99}=+0.242460614\) \(a_{100}=-0.686117172\)

Showing 100 of 1228 available coefficients

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