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: \( 5.6778682089 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.198291214\) \(a_{3}=+0.577350269\) \(a_{4}=-0.960680594\) \(a_{5}=+0.166109708\)
\(a_{6}=+0.114483486\) \(a_{7}=+0.377964473\) \(a_{8}=-0.388785735\) \(a_{9}=+0.333333333\) \(a_{10}=+0.032938096\)
\(a_{11}=+1.021225889\) \(a_{12}=-0.554649200\) \(a_{13}=+1.226738330\) \(a_{14}=+0.074947034\) \(a_{15}=+0.095903485\)
\(a_{16}=+0.883587799\) \(a_{17}=+0.252813249\) \(a_{18}=+0.066097071\) \(a_{19}=+1.597186398\) \(a_{20}=-0.159578373\)
\(a_{21}=+0.218217890\) \(a_{22}=+0.202500121\) \(a_{23}=-1.007844796\) \(a_{24}=-0.224465549\) \(a_{25}=-0.972407565\)
\(a_{26}=+0.243251433\) \(a_{27}=+0.192450090\) \(a_{28}=-0.363103135\) \(a_{29}=+1.131295733\) \(a_{30}=+0.019016818\)
\(a_{31}=+0.425527397\) \(a_{32}=+0.563993433\) \(a_{33}=+0.589605042\) \(a_{34}=+0.050130646\) \(a_{35}=+0.062783568\)
\(a_{36}=-0.320226865\) \(a_{37}=-1.219340529\) \(a_{38}=+0.316708030\) \(a_{39}=+0.708257705\) \(a_{40}=-0.064581085\)
\(a_{41}=+0.658795677\) \(a_{42}=+0.043270690\) \(a_{43}=-1.129919997\) \(a_{44}=-0.981071894\) \(a_{45}=+0.055369903\)
\(a_{46}=-0.199846768\) \(a_{47}=+0.391576541\) \(a_{48}=+0.510139654\) \(a_{49}=+0.142857143\) \(a_{50}=-0.192819877\)
\(a_{51}=+0.145961797\) \(a_{52}=-1.178503708\) \(a_{53}=-0.154323327\) \(a_{54}=+0.038161162\) \(a_{55}=+0.169635535\)
\(a_{56}=-0.146947196\) \(a_{57}=+0.922135997\) \(a_{58}=+0.224326004\) \(a_{59}=+0.686946787\) \(a_{60}=-0.092132617\)
\(a_{61}=+0.669460890\) \(a_{62}=+0.084378344\) \(a_{63}=+0.125988158\) \(a_{64}=-0.771752857\) \(a_{65}=+0.203773146\)
\(a_{66}=+0.116913500\) \(a_{67}=-0.019331223\) \(a_{68}=-0.242872782\) \(a_{69}=-0.581879464\) \(a_{70}=+0.012449430\)
\(a_{71}=+1.912762749\) \(a_{72}=-0.129595245\) \(a_{73}=-0.736167065\) \(a_{74}=-0.241784514\) \(a_{75}=-0.561419769\)
\(a_{76}=-1.534385979\) \(a_{77}=+0.385987105\) \(a_{78}=+0.140441280\) \(a_{79}=+0.417595028\) \(a_{80}=+0.146772512\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.130633395\) \(a_{83}=-1.825888729\) \(a_{84}=-0.209637693\) \(a_{85}=+0.041994735\)
\(a_{86}=-0.224053208\) \(a_{87}=+0.653153896\) \(a_{88}=-0.397038058\) \(a_{89}=+0.363135803\) \(a_{90}=+0.010979365\)
\(a_{91}=+0.463663506\) \(a_{92}=+0.968216938\) \(a_{93}=+0.245678357\) \(a_{94}=+0.077646188\) \(a_{95}=+0.265308167\)
\(a_{96}=+0.325621760\) \(a_{97}=+0.067380168\) \(a_{98}=+0.028327316\) \(a_{99}=+0.340408630\) \(a_{100}=+0.934173077\)

Showing 100 of 262 available coefficients

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