Properties

Level $31$
Weight $0$
Character 31.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.06284037124 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.590846401\) \(a_{3}=+0.388403717\) \(a_{4}=-0.650900530\) \(a_{5}=-0.879001361\)
\(a_{6}=+0.229486939\) \(a_{7}=+1.679730476\) \(a_{8}=-0.975428637\) \(a_{9}=-0.849142552\) \(a_{10}=-0.519354791\)
\(a_{11}=-0.088824975\) \(a_{12}=-0.252812186\) \(a_{13}=+1.082079489\) \(a_{14}=+0.992462707\) \(a_{15}=-0.341407396\)
\(a_{16}=+0.074572030\) \(a_{17}=+0.797427513\) \(a_{18}=-0.501712821\) \(a_{19}=-0.757849641\) \(a_{20}=+0.572142452\)
\(a_{21}=+0.652413561\) \(a_{22}=-0.052481917\) \(a_{23}=+0.494927375\) \(a_{24}=-0.378860109\) \(a_{25}=-0.227356608\)
\(a_{26}=+0.639342772\) \(a_{27}=-0.718213841\) \(a_{28}=-1.093337457\) \(a_{29}=-0.943350565\) \(a_{30}=-0.201719331\)
\(a_{31}=+0.179605302\) \(a_{32}=+1.019489253\) \(a_{33}=-0.034499951\) \(a_{34}=+0.471157176\) \(a_{35}=-1.476485374\)
\(a_{36}=+0.552707337\) \(a_{37}=-1.215652022\) \(a_{38}=-0.447772733\) \(a_{39}=+0.420283696\) \(a_{40}=+0.857403099\)
\(a_{41}=-0.269380962\) \(a_{42}=+0.385476205\) \(a_{43}=+0.377861458\) \(a_{44}=+0.057816224\) \(a_{45}=+0.746397459\)
\(a_{46}=+0.292426059\) \(a_{47}=+0.119915444\) \(a_{48}=+0.028964054\) \(a_{49}=+1.821494471\) \(a_{50}=-0.134332834\)
\(a_{51}=+0.309723810\) \(a_{52}=-0.704326113\) \(a_{53}=+0.808908056\) \(a_{54}=-0.424354063\) \(a_{55}=+0.078077274\)
\(a_{56}=-1.638457209\) \(a_{57}=-0.294351618\) \(a_{58}=-0.557375287\) \(a_{59}=+1.230647150\) \(a_{60}=+0.222222255\)
\(a_{61}=-0.469920578\) \(a_{62}=+0.106119146\) \(a_{63}=-1.426330623\) \(a_{64}=+0.527789526\) \(a_{65}=-0.951149343\)
\(a_{66}=-0.020384172\) \(a_{67}=-0.630716065\) \(a_{68}=-0.519045991\) \(a_{69}=+0.192231632\) \(a_{70}=-0.872376070\)
\(a_{71}=+0.035235704\) \(a_{72}=+0.828277963\) \(a_{73}=+1.098117823\) \(a_{74}=-0.718263623\) \(a_{75}=-0.088306152\)
\(a_{76}=+0.493284733\) \(a_{77}=-0.149202018\) \(a_{78}=+0.248323109\) \(a_{79}=+1.512095070\) \(a_{80}=-0.065548916\)
\(a_{81}=+0.570185627\) \(a_{82}=-0.159162772\) \(a_{83}=-0.438852135\) \(a_{84}=-0.424656333\) \(a_{85}=-0.700939869\)
\(a_{86}=+0.223258083\) \(a_{87}=-0.366400866\) \(a_{88}=+0.086642425\) \(a_{89}=-1.176721476\) \(a_{90}=+0.441006253\)
\(a_{91}=+1.817601894\) \(a_{92}=-0.322148491\) \(a_{93}=+0.069759367\) \(a_{94}=+0.070851609\) \(a_{95}=+0.666150865\)
\(a_{96}=+0.395973416\) \(a_{97}=-0.589827067\) \(a_{98}=+1.076223453\) \(a_{99}=+0.075425066\) \(a_{100}=+0.147986537\)

Showing 100 of 546 available coefficients

Rows: Cols: