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: \( 3.73514871954 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.702414760\) \(a_{3}=-0.577350269\) \(a_{4}=-0.506613504\) \(a_{5}=-0.603985018\)
\(a_{6}=-0.405539351\) \(a_{7}=+0.377964473\) \(a_{8}=-1.058267564\) \(a_{9}=+0.333333333\) \(a_{10}=-0.424247991\)
\(a_{11}=-0.852292199\) \(a_{12}=+0.292493443\) \(a_{13}=-1.235047081\) \(a_{14}=+0.265487825\) \(a_{15}=+0.348710912\)
\(a_{16}=-0.236729253\) \(a_{17}=+1.683850761\) \(a_{18}=+0.234138253\) \(a_{19}=-0.175648295\) \(a_{20}=+0.305986966\)
\(a_{21}=-0.218217890\) \(a_{22}=-0.598662621\) \(a_{23}=-0.381664200\) \(a_{24}=+0.610991063\) \(a_{25}=-0.635202099\)
\(a_{26}=-0.867515300\) \(a_{27}=-0.192450090\) \(a_{28}=-0.191481906\) \(a_{29}=-0.912380136\) \(a_{30}=+0.244939692\)
\(a_{31}=+0.291339251\) \(a_{32}=+0.891985442\) \(a_{33}=+0.492071131\) \(a_{34}=+1.182761629\) \(a_{35}=-0.228284879\)
\(a_{36}=-0.168871168\) \(a_{37}=-1.013259305\) \(a_{38}=-0.123377955\) \(a_{39}=+0.713054765\) \(a_{40}=+0.639177753\)
\(a_{41}=+1.400914283\) \(a_{42}=-0.153279467\) \(a_{43}=-1.811369754\) \(a_{44}=+0.431782738\) \(a_{45}=-0.201328339\)
\(a_{46}=-0.268086568\) \(a_{47}=-0.211068361\) \(a_{48}=+0.136675698\) \(a_{49}=+0.142857143\) \(a_{50}=-0.446175330\)
\(a_{51}=-0.972171690\) \(a_{52}=+0.625691530\) \(a_{53}=-0.289935773\) \(a_{54}=-0.135179784\) \(a_{55}=+0.514771719\)
\(a_{56}=-0.399987542\) \(a_{57}=+0.101410591\) \(a_{58}=-0.640869274\) \(a_{59}=+0.966785917\) \(a_{60}=-0.176661657\)
\(a_{61}=-1.439320369\) \(a_{62}=+0.204640990\) \(a_{63}=+0.125988158\) \(a_{64}=+0.863272994\) \(a_{65}=+0.745949933\)
\(a_{66}=+0.345638025\) \(a_{67}=+1.510452344\) \(a_{68}=-0.853061535\) \(a_{69}=+0.220353929\) \(a_{70}=-0.160350668\)
\(a_{71}=+0.393139135\) \(a_{72}=-0.352755855\) \(a_{73}=-0.616359641\) \(a_{74}=-0.711728292\) \(a_{75}=+0.366734103\)
\(a_{76}=+0.088985799\) \(a_{77}=-0.322136172\) \(a_{78}=+0.500860192\) \(a_{79}=-0.222737397\) \(a_{80}=+0.142980922\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.984022870\) \(a_{83}=+0.350194879\) \(a_{84}=+0.110552130\) \(a_{85}=-1.017020631\)
\(a_{86}=-1.272332852\) \(a_{87}=+0.526762917\) \(a_{88}=+0.901953189\) \(a_{89}=-0.885812870\) \(a_{90}=-0.141415997\)
\(a_{91}=-0.466803919\) \(a_{92}=+0.193356238\) \(a_{93}=-0.168204795\) \(a_{94}=-0.148257532\) \(a_{95}=+0.106088939\)
\(a_{96}=-0.514988035\) \(a_{97}=-1.766386610\) \(a_{98}=+0.100344966\) \(a_{99}=-0.284097400\) \(a_{100}=+0.321801961\)

Showing 100 of 222 available coefficients

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