Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 11.7145309917 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.817152512\) \(a_{3}=+0.577350269\) \(a_{4}=+2.302043252\) \(a_{5}=+0.234803353\)
\(a_{6}=+1.049133492\) \(a_{7}=-0.919382583\) \(a_{8}=+2.366011166\) \(a_{9}=+0.333333332\) \(a_{10}=+0.426673509\)
\(a_{11}=+0.029258336\) \(a_{12}=+1.329085444\) \(a_{13}=+0.614033792\) \(a_{14}=-1.670654577\) \(a_{15}=+0.135544176\)
\(a_{16}=+1.997461614\) \(a_{17}=-1.529578277\) \(a_{18}=+0.605717504\) \(a_{19}=-0.416335213\) \(a_{20}=+0.540527474\)
\(a_{21}=-0.530805782\) \(a_{22}=+0.053166916\) \(a_{23}=-0.530533639\) \(a_{24}=+1.366017183\) \(a_{25}=-0.944867386\)
\(a_{26}=+1.115794415\) \(a_{27}=+0.192450090\) \(a_{28}=-2.116458471\) \(a_{29}=-0.259102337\) \(a_{30}=+0.246340061\)
\(a_{31}=+1.596627835\) \(a_{32}=+1.263496360\) \(a_{33}=+0.016892326\) \(a_{34}=-2.779477009\) \(a_{35}=-0.215874113\)
\(a_{36}=+0.767347751\) \(a_{37}=+0.615935220\) \(a_{38}=-0.756544578\) \(a_{39}=+0.354513010\) \(a_{40}=+0.555547354\)
\(a_{41}=+0.901486667\) \(a_{42}=-0.964555060\) \(a_{43}=-0.437298773\) \(a_{44}=+0.067354028\) \(a_{45}=+0.078267784\)
\(a_{46}=-0.964060534\) \(a_{47}=+0.727979297\) \(a_{48}=+1.153176266\) \(a_{49}=-0.154735667\) \(a_{50}=-1.716968145\)
\(a_{51}=-0.883102429\) \(a_{52}=+1.413534083\) \(a_{53}=+1.873566114\) \(a_{54}=+0.349711156\) \(a_{55}=+0.006869960\)
\(a_{56}=-2.175269445\) \(a_{57}=-0.240371232\) \(a_{58}=-0.470828478\) \(a_{59}=+0.064845723\) \(a_{60}=+0.312073704\)
\(a_{61}=-1.217957547\) \(a_{62}=+2.901316309\) \(a_{63}=-0.306460861\) \(a_{64}=+0.298605704\) \(a_{65}=+0.144177370\)
\(a_{66}=+0.030695932\) \(a_{67}=+1.210282347\) \(a_{68}=-3.521155350\) \(a_{69}=-0.306303738\) \(a_{70}=-0.392276188\)
\(a_{71}=+0.593848160\) \(a_{72}=+0.788670389\) \(a_{73}=+0.785250931\) \(a_{74}=+1.119248234\) \(a_{75}=-0.545519446\)
\(a_{76}=-0.958421674\) \(a_{77}=-0.026899628\) \(a_{78}=+0.644204220\) \(a_{79}=-1.232977830\) \(a_{80}=+0.468986773\)
\(a_{81}=+0.111111102\) \(a_{82}=+1.638138793\) \(a_{83}=-0.286928967\) \(a_{84}=-1.221937903\) \(a_{85}=-0.359150180\)
\(a_{86}=-0.794638552\) \(a_{87}=-0.149592680\) \(a_{88}=+0.069225679\) \(a_{89}=+1.656938148\) \(a_{90}=+0.142224330\)
\(a_{91}=-0.564532491\) \(a_{92}=-1.221310993\) \(a_{93}=+0.921813437\) \(a_{94}=+1.322848724\) \(a_{95}=-0.097757123\)
\(a_{96}=+0.729480877\) \(a_{97}=-0.146923382\) \(a_{98}=-0.281179339\) \(a_{99}=+0.009750738\) \(a_{100}=-2.175125037\)

Showing 100 of 5000 available coefficients

Rows: Cols: