Properties

Level $21$
Weight $0$
Character 21.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.61592856746 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.320637441\) \(a_{3}=-0.577350269\) \(a_{4}=+0.744083252\) \(a_{5}=+1.643771697\)
\(a_{6}=-0.762470382\) \(a_{7}=-0.377964473\) \(a_{8}=-0.337973239\) \(a_{9}=+0.333333333\) \(a_{10}=+2.170826448\)
\(a_{11}=-0.836782893\) \(a_{12}=-0.429596666\) \(a_{13}=+0.702731514\) \(a_{14}=-0.499154035\) \(a_{15}=-0.949032032\)
\(a_{16}=-1.190423366\) \(a_{17}=-0.146210861\) \(a_{18}=+0.440212480\) \(a_{19}=-0.044753048\) \(a_{20}=+1.223102989\)
\(a_{21}=+0.218217890\) \(a_{22}=-1.105086819\) \(a_{23}=+1.064221971\) \(a_{24}=+0.195128941\) \(a_{25}=+1.701985391\)
\(a_{26}=+0.928053549\) \(a_{27}=-0.192450090\) \(a_{28}=-0.281237034\) \(a_{29}=-1.343394234\) \(a_{30}=-1.253327235\)
\(a_{31}=+0.141725017\) \(a_{32}=-1.234144429\) \(a_{33}=+0.483116831\) \(a_{34}=-0.193091537\) \(a_{35}=-0.621287307\)
\(a_{36}=+0.248027748\) \(a_{37}=+0.642697937\) \(a_{38}=-0.059102545\) \(a_{39}=-0.405722236\) \(a_{40}=-0.555550858\)
\(a_{41}=+1.445981228\) \(a_{42}=+0.288186744\) \(a_{43}=-0.127004623\) \(a_{44}=-0.622636166\) \(a_{45}=+0.547923846\)
\(a_{46}=+1.405451411\) \(a_{47}=-1.997283640\) \(a_{48}=+0.687291251\) \(a_{49}=+0.142857142\) \(a_{50}=+2.247705632\)
\(a_{51}=+0.084414882\) \(a_{52}=+0.522890752\) \(a_{53}=-0.854758979\) \(a_{54}=-0.254156799\) \(a_{55}=-1.375480035\)
\(a_{56}=+0.127741879\) \(a_{57}=+0.025838188\) \(a_{58}=-1.774136717\) \(a_{59}=+0.289943396\) \(a_{60}=-0.706158866\)
\(a_{61}=+0.894700126\) \(a_{62}=+0.187167386\) \(a_{63}=-0.125987984\) \(a_{64}=-0.439433959\) \(a_{65}=+1.155130196\)
\(a_{66}=+0.638022441\) \(a_{67}=+0.695105889\) \(a_{68}=-0.108793059\) \(a_{69}=-0.614428858\) \(a_{70}=-0.820495278\)
\(a_{71}=-0.785300452\) \(a_{72}=-0.112657773\) \(a_{73}=+0.237800933\) \(a_{74}=+0.848770878\) \(a_{75}=-0.982641681\)
\(a_{76}=-0.033299964\) \(a_{77}=+0.316274216\) \(a_{78}=-0.535811920\) \(a_{79}=+0.579790718\) \(a_{80}=-1.956784206\)
\(a_{81}=+0.111112161\) \(a_{82}=+1.909616237\) \(a_{83}=+0.597807760\) \(a_{84}=+0.162370278\) \(a_{85}=-0.240337971\)
\(a_{86}=-0.167727014\) \(a_{87}=+0.775609041\) \(a_{88}=+0.282810268\) \(a_{89}=+0.488506036\) \(a_{90}=+0.723608817\)
\(a_{91}=-0.265607304\) \(a_{92}=+0.791869665\) \(a_{93}=-0.081826098\) \(a_{94}=-2.637687895\) \(a_{95}=-0.073563930\)
\(a_{96}=+0.712533791\) \(a_{97}=+0.105831399\) \(a_{98}=+0.188666613\) \(a_{99}=-0.278928178\) \(a_{100}=+1.266419279\)

Showing 100 of 1500 available coefficients

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