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: \( 18.0796004487 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.232591776\) \(a_{3}=+0.577350269\) \(a_{4}=+0.519282486\) \(a_{5}=+1.311538451\)
\(a_{6}=-0.711637194\) \(a_{7}=+1.684803334\) \(a_{8}=+0.592528454\) \(a_{9}=+0.333333333\) \(a_{10}=-1.616591509\)
\(a_{11}=-0.619258432\) \(a_{12}=+0.299807883\) \(a_{13}=-0.070878793\) \(a_{14}=-2.076674733\) \(a_{15}=+0.757217078\)
\(a_{16}=-1.249628186\) \(a_{17}=+0.192168944\) \(a_{18}=-0.410863925\) \(a_{19}=+0.670474241\) \(a_{20}=+0.681058947\)
\(a_{21}=+0.972721658\) \(a_{22}=+0.763292850\) \(a_{23}=+0.519879728\) \(a_{24}=+0.342096463\) \(a_{25}=+0.720133109\)
\(a_{26}=+0.087364617\) \(a_{27}=+0.192450090\) \(a_{28}=+0.874888863\) \(a_{29}=+0.901243049\) \(a_{30}=-0.933339543\)
\(a_{31}=-0.840310613\) \(a_{32}=+0.947752970\) \(a_{33}=-0.357529022\) \(a_{34}=-0.236865859\) \(a_{35}=+2.209684355\)
\(a_{36}=+0.173094162\) \(a_{37}=-1.907726492\) \(a_{38}=-0.826421035\) \(a_{39}=-0.040921890\) \(a_{40}=+0.777123851\)
\(a_{41}=+1.619423939\) \(a_{42}=-1.198968716\) \(a_{43}=+0.411371542\) \(a_{44}=-0.321570058\) \(a_{45}=+0.437179484\)
\(a_{46}=-0.640799477\) \(a_{47}=-0.311362450\) \(a_{48}=-0.721473169\) \(a_{49}=+1.838562273\) \(a_{50}=-0.887630148\)
\(a_{51}=+0.110948791\) \(a_{52}=-0.036806116\) \(a_{53}=+0.704161422\) \(a_{54}=-0.237212398\) \(a_{55}=-0.812181244\)
\(a_{56}=+0.998293915\) \(a_{57}=+0.387098483\) \(a_{58}=-1.110864770\) \(a_{59}=-0.700001649\) \(a_{60}=+0.393209567\)
\(a_{61}=-0.653630914\) \(a_{62}=+1.035759951\) \(a_{63}=+0.561601111\) \(a_{64}=+0.081435669\) \(a_{65}=-0.092960262\)
\(a_{66}=+0.440687332\) \(a_{67}=-0.370408654\) \(a_{68}=+0.099789967\) \(a_{69}=+0.300152701\) \(a_{70}=-2.723638763\)
\(a_{71}=+0.495460624\) \(a_{72}=+0.197509485\) \(a_{73}=-0.486706943\) \(a_{74}=+2.351447984\) \(a_{75}=+0.415769044\)
\(a_{76}=+0.348165530\) \(a_{77}=-1.043328670\) \(a_{78}=+0.050439985\) \(a_{79}=+0.757223453\) \(a_{80}=-1.638935415\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.996088628\) \(a_{83}=+1.759114500\) \(a_{84}=+0.505117321\) \(a_{85}=+0.252036959\)
\(a_{86}=-0.507053180\) \(a_{87}=+0.520332917\) \(a_{88}=-0.366928241\) \(a_{89}=+0.698738401\) \(a_{90}=-0.538863836\)
\(a_{91}=-0.119416826\) \(a_{92}=+0.269964437\) \(a_{93}=-0.485153559\) \(a_{94}=+0.383782795\) \(a_{95}=+0.879352747\)
\(a_{96}=+0.547185433\) \(a_{97}=-0.752618196\) \(a_{98}=-2.266196737\) \(a_{99}=-0.206419477\) \(a_{100}=+0.373952511\)

Showing 100 of 1228 available coefficients

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