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: \( 13.3786205776 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.554382270\) \(a_{3}=-0.577350269\) \(a_{4}=+1.416104241\) \(a_{5}=-1.477310160\)
\(a_{6}=-0.897423022\) \(a_{7}=-0.895829860\) \(a_{8}=+0.646785054\) \(a_{9}=+0.333333333\) \(a_{10}=-2.296304718\)
\(a_{11}=+0.457642291\) \(a_{12}=-0.817588124\) \(a_{13}=-0.818795173\) \(a_{14}=-1.392461155\) \(a_{15}=+0.852921005\)
\(a_{16}=-0.410730813\) \(a_{17}=-0.846571376\) \(a_{18}=+0.518127423\) \(a_{19}=+0.878041578\) \(a_{20}=-2.092025183\)
\(a_{21}=+0.517207611\) \(a_{22}=+0.711351078\) \(a_{23}=-0.016644877\) \(a_{24}=-0.373421525\) \(a_{25}=+1.182445309\)
\(a_{26}=-1.272720409\) \(a_{27}=-0.192450090\) \(a_{28}=-1.268588463\) \(a_{29}=+1.569165075\) \(a_{30}=+1.325772148\)
\(a_{31}=+0.108259908\) \(a_{32}=-1.285252266\) \(a_{33}=-0.264219905\) \(a_{34}=-1.315719108\) \(a_{35}=+1.323418553\)
\(a_{36}=+0.472034747\) \(a_{37}=-0.918214777\) \(a_{38}=+1.364812261\) \(a_{39}=+0.472731506\) \(a_{40}=-0.955502132\)
\(a_{41}=-1.136126130\) \(a_{42}=+0.803938340\) \(a_{43}=-0.107539436\) \(a_{44}=+0.648069202\) \(a_{45}=-0.492436723\)
\(a_{46}=-0.025872503\) \(a_{47}=-0.657643623\) \(a_{48}=+0.237148371\) \(a_{49}=-0.197488872\) \(a_{50}=+1.837972005\)
\(a_{51}=+0.488702696\) \(a_{52}=-1.159499005\) \(a_{53}=-0.292249194\) \(a_{54}=-0.299141110\) \(a_{55}=-0.676079680\)
\(a_{56}=-0.579409087\) \(a_{57}=-0.506937352\) \(a_{58}=+2.439081928\) \(a_{59}=-0.564761457\) \(a_{60}=+1.207831905\)
\(a_{61}=-0.308434848\) \(a_{62}=+0.168276339\) \(a_{63}=-0.298615114\) \(a_{64}=-1.587020314\) \(a_{65}=+1.209614152\)
\(a_{66}=-0.410698737\) \(a_{67}=-0.800545656\) \(a_{68}=-1.198672582\) \(a_{69}=+0.009609925\) \(a_{70}=+2.057098334\)
\(a_{71}=+1.823677163\) \(a_{72}=+0.215595018\) \(a_{73}=-1.110227097\) \(a_{74}=-1.427256768\) \(a_{75}=-0.682685120\)
\(a_{76}=+1.243398399\) \(a_{77}=-0.409969636\) \(a_{78}=+0.734805476\) \(a_{79}=-0.373014372\) \(a_{80}=+0.606809603\)
\(a_{81}=+0.111111106\) \(a_{82}=-1.765974306\) \(a_{83}=-0.637638111\) \(a_{84}=+0.732419888\) \(a_{85}=+1.250480799\)
\(a_{86}=-0.167157388\) \(a_{87}=-0.905957858\) \(a_{88}=+0.295996205\) \(a_{89}=+1.755111359\) \(a_{90}=-0.765434937\)
\(a_{91}=+0.733501035\) \(a_{92}=-0.023570846\) \(a_{93}=-0.062503882\) \(a_{94}=-1.022229630\) \(a_{95}=-1.297139744\)
\(a_{96}=+0.742040726\) \(a_{97}=-1.615875174\) \(a_{98}=-0.306973134\) \(a_{99}=+0.152547884\) \(a_{100}=+1.674466305\)

Showing 100 of 5000 available coefficients

Rows: Cols: