Properties

Level $21$
Weight $0$
Character 21.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.08530975931 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.832823106\) \(a_{3}=+0.577350269\) \(a_{4}=-0.306405673\) \(a_{5}=+0.147792305\)
\(a_{6}=+0.480830645\) \(a_{7}=-0.377964473\) \(a_{8}=-1.088004831\) \(a_{9}=+0.333333333\) \(a_{10}=+0.123084846\)
\(a_{11}=+0.758648692\) \(a_{12}=-0.176903398\) \(a_{13}=+0.831641906\) \(a_{14}=-0.314777547\) \(a_{15}=+0.085327927\)
\(a_{16}=-0.599709890\) \(a_{17}=+1.574592613\) \(a_{18}=+0.277607702\) \(a_{19}=-1.724217983\) \(a_{20}=-0.045284401\)
\(a_{21}=-0.218217890\) \(a_{22}=+0.631820160\) \(a_{23}=-0.798267001\) \(a_{24}=-0.628159882\) \(a_{25}=-0.978157435\)
\(a_{26}=+0.692610595\) \(a_{27}=+0.192450090\) \(a_{28}=+0.115810459\) \(a_{29}=-0.463466458\) \(a_{30}=+0.071063070\)
\(a_{31}=+1.071805267\) \(a_{32}=+0.588552576\) \(a_{33}=+0.438006026\) \(a_{34}=+1.311357110\) \(a_{35}=-0.055860240\)
\(a_{36}=-0.102135224\) \(a_{37}=+0.475190572\) \(a_{38}=-1.435968570\) \(a_{39}=+0.480148679\) \(a_{40}=-0.160798741\)
\(a_{41}=-0.374765854\) \(a_{42}=-0.181736900\) \(a_{43}=-1.157444153\) \(a_{44}=-0.232454269\) \(a_{45}=+0.049264095\)
\(a_{46}=-0.664815215\) \(a_{47}=+0.413883768\) \(a_{48}=-0.346242661\) \(a_{49}=+0.142857175\) \(a_{50}=-0.814632106\)
\(a_{51}=+0.909091428\) \(a_{52}=-0.254819766\) \(a_{53}=+1.229902123\) \(a_{54}=+0.160276825\) \(a_{55}=+0.112122330\)
\(a_{56}=+0.411226976\) \(a_{57}=-0.995477859\) \(a_{58}=-0.385985102\) \(a_{59}=-0.170885923\) \(a_{60}=-0.026145216\)
\(a_{61}=+0.445718012\) \(a_{62}=+0.892623109\) \(a_{63}=-0.125988221\) \(a_{64}=+1.089870083\) \(a_{65}=+0.122910304\)
\(a_{66}=+0.364781556\) \(a_{67}=-1.399358509\) \(a_{68}=-0.482464223\) \(a_{69}=-0.460879137\) \(a_{70}=-0.046521793\)
\(a_{71}=+1.041025266\) \(a_{72}=-0.362668563\) \(a_{73}=+0.891254026\) \(a_{74}=+0.395754027\) \(a_{75}=-0.564742533\)
\(a_{76}=+0.528308074\) \(a_{77}=-0.286742290\) \(a_{78}=+0.399878663\) \(a_{79}=-0.525979921\) \(a_{80}=-0.088632718\)
\(a_{81}=+0.111108882\) \(a_{82}=-0.312113043\) \(a_{83}=-0.627667586\) \(a_{84}=+0.066863778\) \(a_{85}=+0.232711322\)
\(a_{86}=-0.963944897\) \(a_{87}=-0.267578405\) \(a_{88}=-0.825418766\) \(a_{89}=-0.430236865\) \(a_{90}=+0.041030434\)
\(a_{91}=-0.314355033\) \(a_{92}=+0.244596737\) \(a_{93}=+0.618820427\) \(a_{94}=+0.344697042\) \(a_{95}=-0.254768781\)
\(a_{96}=+0.339800879\) \(a_{97}=-0.279855579\) \(a_{98}=+0.118973656\) \(a_{99}=+0.252879259\) \(a_{100}=+0.299717878\)

Showing 100 of 1500 available coefficients

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