Properties

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

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.3714667269 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.544112166\) \(a_{3}=+1.491819817\) \(a_{4}=+1.384282381\) \(a_{5}=-0.376979188\)
\(a_{6}=-2.303537129\) \(a_{7}=-1.157191404\) \(a_{8}=-0.593375100\) \(a_{9}=+1.225526366\) \(a_{10}=+0.582098151\)
\(a_{11}=-1.571158725\) \(a_{12}=+2.065099889\) \(a_{13}=-1.193883683\) \(a_{14}=+1.786833326\) \(a_{15}=-0.562385023\)
\(a_{16}=-0.468044670\) \(a_{17}=+0.726834349\) \(a_{18}=-1.892350172\) \(a_{19}=-0.138269545\) \(a_{20}=-0.521845648\)
\(a_{21}=-1.726321069\) \(a_{22}=+2.426045303\) \(a_{23}=-0.294973329\) \(a_{24}=-0.885208733\) \(a_{25}=-0.857886692\)
\(a_{26}=+1.843490319\) \(a_{27}=+0.336444703\) \(a_{28}=-1.601879673\) \(a_{29}=+1.679098437\) \(a_{30}=+0.868385557\)
\(a_{31}=-0.179605302\) \(a_{32}=+1.316088570\) \(a_{33}=-2.343885722\) \(a_{34}=-1.122313760\) \(a_{35}=+0.436237076\)
\(a_{36}=+1.696474557\) \(a_{37}=-1.521444225\) \(a_{38}=+0.213503686\) \(a_{39}=-1.781059337\) \(a_{40}=+0.223690063\)
\(a_{41}=+1.028076921\) \(a_{42}=+2.665633365\) \(a_{43}=+1.183049920\) \(a_{44}=-2.174927342\) \(a_{45}=-0.461997935\)
\(a_{46}=+0.455471906\) \(a_{47}=-0.321805367\) \(a_{48}=-0.698238314\) \(a_{49}=+0.339091946\) \(a_{50}=+1.324673278\)
\(a_{51}=+1.084305885\) \(a_{52}=-1.652672147\) \(a_{53}=+0.059371411\) \(a_{54}=-0.519508359\) \(a_{55}=+0.592294141\)
\(a_{56}=+0.686648565\) \(a_{57}=-0.206273247\) \(a_{58}=-2.592716324\) \(a_{59}=-0.495528763\) \(a_{60}=-0.778499679\)
\(a_{61}=-0.284921999\) \(a_{62}=+0.277330732\) \(a_{63}=-1.418168577\) \(a_{64}=-1.564143702\) \(a_{65}=+0.450069301\)
\(a_{66}=+3.619222459\) \(a_{67}=+1.697551248\) \(a_{68}=+1.006143983\) \(a_{69}=-0.440047057\) \(a_{70}=-0.673598976\)
\(a_{71}=-1.338164450\) \(a_{72}=-0.727196830\) \(a_{73}=+0.407868655\) \(a_{74}=+2.349280538\) \(a_{75}=-1.279812367\)
\(a_{76}=-0.191404095\) \(a_{77}=+1.818131372\) \(a_{78}=+2.750155391\) \(a_{79}=-0.307589185\) \(a_{80}=+0.176443100\)
\(a_{81}=-0.723611492\) \(a_{82}=-1.587466082\) \(a_{83}=-0.152918626\) \(a_{84}=-2.389715840\) \(a_{85}=-0.274001423\)
\(a_{86}=-1.826761774\) \(a_{87}=+2.504912323\) \(a_{88}=+0.932286466\) \(a_{89}=+0.028272441\) \(a_{90}=+0.713376631\)
\(a_{91}=+1.381551935\) \(a_{92}=-0.408326382\) \(a_{93}=-0.267938749\) \(a_{94}=+0.496903582\) \(a_{95}=+0.052124741\)
\(a_{96}=+1.963367009\) \(a_{97}=-1.030044243\) \(a_{98}=-0.523595999\) \(a_{99}=-1.925496444\) \(a_{100}=-1.187557432\)

Showing 100 of 546 available coefficients

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