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: \( 5.71234657181 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.710841087\) \(a_{3}=-0.577350269\) \(a_{4}=+1.926977225\) \(a_{5}=-1.778601733\)
\(a_{6}=-0.987754562\) \(a_{7}=-0.377964473\) \(a_{8}=+1.585910723\) \(a_{9}=+0.333333333\) \(a_{10}=-3.042904922\)
\(a_{11}=-0.805841333\) \(a_{12}=-1.112540820\) \(a_{13}=-1.135522031\) \(a_{14}=-0.646637150\) \(a_{15}=+1.026876189\)
\(a_{16}=+0.786264000\) \(a_{17}=+0.416655624\) \(a_{18}=+0.570280362\) \(a_{19}=-0.290138706\) \(a_{20}=-3.427325032\)
\(a_{21}=+0.218217890\) \(a_{22}=-1.378666462\) \(a_{23}=+1.484687677\) \(a_{24}=-0.915625983\) \(a_{25}=+2.163424125\)
\(a_{26}=-1.942697746\) \(a_{27}=-0.192450090\) \(a_{28}=-0.728328931\) \(a_{29}=-0.345385438\) \(a_{30}=+1.756821976\)
\(a_{31}=-0.232126335\) \(a_{32}=-0.240737966\) \(a_{33}=+0.465252710\) \(a_{34}=+0.712831561\) \(a_{35}=+0.672248267\)
\(a_{36}=+0.642325742\) \(a_{37}=-0.504023058\) \(a_{38}=-0.496381219\) \(a_{39}=+0.655593950\) \(a_{40}=-2.820703561\)
\(a_{41}=+1.118559557\) \(a_{42}=+0.373336133\) \(a_{43}=-1.505550936\) \(a_{44}=-1.552837895\) \(a_{45}=-0.592867244\)
\(a_{46}=+2.540064679\) \(a_{47}=-0.273757320\) \(a_{48}=-0.453949732\) \(a_{49}=+0.142857143\) \(a_{50}=+3.701274881\)
\(a_{51}=-0.240556237\) \(a_{52}=-2.188125092\) \(a_{53}=-0.519572590\) \(a_{54}=-0.329251521\) \(a_{55}=+1.433270791\)
\(a_{56}=-0.599417911\) \(a_{57}=+0.167511660\) \(a_{58}=-0.590899598\) \(a_{59}=-1.783628491\) \(a_{60}=+1.978767030\)
\(a_{61}=+0.010201407\) \(a_{62}=-0.397131272\) \(a_{63}=-0.125988158\) \(a_{64}=-1.198128404\) \(a_{65}=+2.019641452\)
\(a_{66}=+0.795973453\) \(a_{67}=-0.443188188\) \(a_{68}=+0.802885899\) \(a_{69}=-0.857184830\) \(a_{70}=+1.150109955\)
\(a_{71}=+0.420738713\) \(a_{72}=+0.528636908\) \(a_{73}=-0.912375010\) \(a_{74}=-0.862303356\) \(a_{75}=-1.249053501\)
\(a_{76}=-0.559090678\) \(a_{77}=+0.304579395\) \(a_{78}=+1.121617067\) \(a_{79}=-0.514832314\) \(a_{80}=-1.398450514\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.913677648\) \(a_{83}=+0.789023769\) \(a_{84}=+0.420500905\) \(a_{85}=-0.741064415\)
\(a_{86}=-2.575758399\) \(a_{87}=+0.199408375\) \(a_{88}=-1.277992411\) \(a_{89}=-1.050129227\) \(a_{90}=-1.014301641\)
\(a_{91}=+0.429186986\) \(a_{92}=+2.860959340\) \(a_{93}=+0.134018202\) \(a_{94}=-0.468355270\) \(a_{95}=+0.516041205\)
\(a_{96}=+0.138990129\) \(a_{97}=+0.813116438\) \(a_{98}=+0.244405870\) \(a_{99}=-0.268613778\) \(a_{100}=+4.168869016\)

Showing 100 of 240 available coefficients

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