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: \( 12.6279481097 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.261193355\) \(a_{3}=+0.577350269\) \(a_{4}=+0.590608680\) \(a_{5}=-0.964252322\)
\(a_{6}=-0.728150323\) \(a_{7}=-1.423650889\) \(a_{8}=+0.516321613\) \(a_{9}=+0.333333334\) \(a_{10}=+1.216108618\)
\(a_{11}=+0.563389167\) \(a_{12}=+0.340988015\) \(a_{13}=+0.065464102\) \(a_{14}=+1.795497536\) \(a_{15}=-0.556703797\)
\(a_{16}=-1.241828479\) \(a_{17}=+1.216116207\) \(a_{18}=-0.420397785\) \(a_{19}=+1.420303037\) \(a_{20}=-0.569495791\)
\(a_{21}=-0.821945224\) \(a_{22}=-0.710542655\) \(a_{23}=+1.162116700\) \(a_{24}=+0.298098422\) \(a_{25}=-0.070217459\)
\(a_{26}=-0.082562501\) \(a_{27}=+0.192450090\) \(a_{28}=-0.840820572\) \(a_{29}=-0.022332684\) \(a_{30}=+0.702120640\)
\(a_{31}=-0.943160361\) \(a_{32}=+1.049815769\) \(a_{33}=+0.325272879\) \(a_{34}=-1.533514532\) \(a_{35}=+1.372758675\)
\(a_{36}=+0.196869560\) \(a_{37}=+0.180824215\) \(a_{38}=-1.791276753\) \(a_{39}=+0.037795539\) \(a_{40}=-0.497864314\)
\(a_{41}=+1.170039893\) \(a_{42}=+1.036631854\) \(a_{43}=+0.031397316\) \(a_{44}=+0.332742524\) \(a_{45}=-0.321417440\)
\(a_{46}=-1.465653861\) \(a_{47}=-0.157456259\) \(a_{48}=-0.716947828\) \(a_{49}=+1.026781857\) \(a_{50}=+0.088557792\)
\(a_{51}=+0.702013703\) \(a_{52}=+0.038663479\) \(a_{53}=+0.530428386\) \(a_{54}=-0.242716758\) \(a_{55}=-0.543249325\)
\(a_{56}=-0.735061772\) \(a_{57}=+0.820012366\) \(a_{58}=+0.028165965\) \(a_{59}=-0.748989969\) \(a_{60}=-0.328798807\)
\(a_{61}=+0.134094441\) \(a_{62}=+1.189508098\) \(a_{63}=-0.474549653\) \(a_{64}=-0.082230605\) \(a_{65}=-0.063123614\)
\(a_{66}=-0.410231992\) \(a_{67}=+0.958357397\) \(a_{68}=+0.718134922\) \(a_{69}=+0.670948388\) \(a_{70}=-1.731314119\)
\(a_{71}=-0.787425391\) \(a_{72}=+0.172107204\) \(a_{73}=-0.132421749\) \(a_{74}=-0.228054301\) \(a_{75}=-0.040540063\)
\(a_{76}=+0.838843308\) \(a_{77}=-0.802069472\) \(a_{78}=-0.047667495\) \(a_{79}=+1.946480343\) \(a_{80}=+1.197398976\)
\(a_{81}=+0.111111123\) \(a_{82}=-1.475646563\) \(a_{83}=-0.590803265\) \(a_{84}=-0.485447961\) \(a_{85}=-1.172456915\)
\(a_{86}=-0.039598083\) \(a_{87}=-0.012893879\) \(a_{88}=+0.290889934\) \(a_{89}=+1.199082459\) \(a_{90}=+0.405369698\)
\(a_{91}=-0.093197680\) \(a_{92}=+0.686355886\) \(a_{93}=-0.544533911\) \(a_{94}=+0.198583287\) \(a_{95}=-1.369530196\)
\(a_{96}=+0.606110841\) \(a_{97}=+1.299054621\) \(a_{98}=-1.294969951\) \(a_{99}=+0.187797999\) \(a_{100}=-0.041470863\)

Showing 100 of 5000 available coefficients

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