Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 15.7994939261 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.889792333\) \(a_{3}=-0.577350269\) \(a_{4}=+2.571315061\) \(a_{5}=+0.584802103\)
\(a_{6}=-1.091072112\) \(a_{7}=-0.031045690\) \(a_{8}=+2.969459154\) \(a_{9}=+0.333333333\) \(a_{10}=+1.105154530\)
\(a_{11}=+0.084933084\) \(a_{12}=-1.484549442\) \(a_{13}=+1.525384353\) \(a_{14}=-0.058669908\) \(a_{15}=-0.337635651\)
\(a_{16}=+3.040346080\) \(a_{17}=-0.676827005\) \(a_{18}=+0.629930778\) \(a_{19}=+0.047009194\) \(a_{20}=+1.503710454\)
\(a_{21}=+0.017924238\) \(a_{22}=+0.160505890\) \(a_{23}=+0.837134340\) \(a_{24}=-1.714418042\) \(a_{25}=-0.658006501\)
\(a_{26}=+2.882659654\) \(a_{27}=-0.192450090\) \(a_{28}=-0.079828251\) \(a_{29}=-1.081434614\) \(a_{30}=-0.638061265\)
\(a_{31}=-0.735142427\) \(a_{32}=+2.776163557\) \(a_{33}=-0.049036139\) \(a_{34}=-1.279062484\) \(a_{35}=-0.018155585\)
\(a_{36}=+0.857105020\) \(a_{37}=-0.829806038\) \(a_{38}=+0.088837615\) \(a_{39}=-0.880681067\) \(a_{40}=+1.736545957\)
\(a_{41}=-0.612663305\) \(a_{42}=+0.033873087\) \(a_{43}=-0.720997173\) \(a_{44}=+0.218389717\) \(a_{45}=+0.194934034\)
\(a_{46}=+1.582010058\) \(a_{47}=+0.237066167\) \(a_{48}=-1.755344628\) \(a_{49}=-0.999036165\) \(a_{50}=-1.243495640\)
\(a_{51}=+0.390766253\) \(a_{52}=+3.922243759\) \(a_{53}=-0.943645155\) \(a_{54}=-0.363690704\) \(a_{55}=+0.049669046\)
\(a_{56}=-0.092188909\) \(a_{57}=-0.027140771\) \(a_{58}=-2.043686842\) \(a_{59}=+1.035201493\) \(a_{60}=-0.868167636\)
\(a_{61}=+1.609383235\) \(a_{62}=-1.389266522\) \(a_{63}=-0.010348563\) \(a_{64}=+2.206026524\) \(a_{65}=+0.892047977\)
\(a_{66}=-0.092668119\) \(a_{67}=-1.293184105\) \(a_{68}=-1.740335470\) \(a_{69}=-0.483319737\) \(a_{70}=-0.034310285\)
\(a_{71}=+1.640049692\) \(a_{72}=+0.989819718\) \(a_{73}=+0.011358524\) \(a_{74}=-1.568161089\) \(a_{75}=+0.379900230\)
\(a_{76}=+0.120875449\) \(a_{77}=-0.002636806\) \(a_{78}=-1.664304327\) \(a_{79}=+1.447392154\) \(a_{80}=+1.778000781\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.157806416\) \(a_{83}=-0.113206627\) \(a_{84}=+0.046088862\) \(a_{85}=-0.395809855\)
\(a_{86}=-1.362534929\) \(a_{87}=+0.624366565\) \(a_{88}=+0.252205323\) \(a_{89}=-0.952862803\) \(a_{90}=+0.368384843\)
\(a_{91}=-0.047356610\) \(a_{92}=+2.152536137\) \(a_{93}=+0.424434678\) \(a_{94}=+0.448005824\) \(a_{95}=+0.027491076\)
\(a_{96}=-1.602818777\) \(a_{97}=+1.246376241\) \(a_{98}=-1.887970885\) \(a_{99}=+0.028311028\) \(a_{100}=-1.691942025\)

Showing 100 of 1228 available coefficients

Rows: Cols: