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: \( 0.924007217602 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.378351052\) \(a_{3}=-0.577350268\) \(a_{4}=-0.856850481\) \(a_{5}=+0.526858199\)
\(a_{6}=-0.218441086\) \(a_{7}=+0.377964473\) \(a_{8}=-0.702541328\) \(a_{9}=+0.333333337\) \(a_{10}=+0.199337345\)
\(a_{11}=+0.293224125\) \(a_{12}=+0.494702867\) \(a_{13}=+0.344102335\) \(a_{14}=+0.143003255\) \(a_{15}=-0.304181772\)
\(a_{16}=+0.591043203\) \(a_{17}=-1.185899641\) \(a_{18}=+0.126117103\) \(a_{19}=-0.387933391\) \(a_{20}=-0.451438881\)
\(a_{21}=-0.218217878\) \(a_{22}=+0.110941975\) \(a_{23}=-0.387942042\) \(a_{24}=+0.405612315\) \(a_{25}=-0.722420530\)
\(a_{26}=+0.130191583\) \(a_{27}=-0.192449879\) \(a_{28}=-0.323859118\) \(a_{29}=+1.795709976\) \(a_{30}=-0.115087543\)
\(a_{31}=+1.242013048\) \(a_{32}=+0.926163199\) \(a_{33}=-0.169293044\) \(a_{34}=-0.448686449\) \(a_{35}=+0.199133682\)
\(a_{36}=-0.285616763\) \(a_{37}=-0.842517680\) \(a_{38}=-0.146774972\) \(a_{39}=-0.198667670\) \(a_{40}=-0.370139481\)
\(a_{41}=+0.034461082\) \(a_{42}=-0.082562878\) \(a_{43}=+0.657716899\) \(a_{44}=-0.251248997\) \(a_{45}=+0.175618655\)
\(a_{46}=-0.146778056\) \(a_{47}=-1.220231391\) \(a_{48}=-0.341238949\) \(a_{49}=+0.142857175\) \(a_{50}=-0.273328509\)
\(a_{51}=+0.684679530\) \(a_{52}=-0.294844280\) \(a_{53}=-0.039758492\) \(a_{54}=-0.072813699\) \(a_{55}=+0.154487596\)
\(a_{56}=-0.265535676\) \(a_{57}=+0.223973492\) \(a_{58}=+0.679408889\) \(a_{59}=-0.113229023\) \(a_{60}=+0.260638478\)
\(a_{61}=+1.002747647\) \(a_{62}=+0.469916939\) \(a_{63}=+0.125988167\) \(a_{64}=-0.240628412\) \(a_{65}=+0.181292995\)
\(a_{66}=-0.064052163\) \(a_{67}=-0.104528040\) \(a_{68}=+1.016138812\) \(a_{69}=+0.223978349\) \(a_{70}=+0.075342405\)
\(a_{71}=-1.854174868\) \(a_{72}=-0.234180371\) \(a_{73}=-0.679742171\) \(a_{74}=-0.318767657\) \(a_{75}=+0.417089561\)
\(a_{76}=+0.332400799\) \(a_{77}=+0.110828408\) \(a_{78}=-0.075166101\) \(a_{79}=-0.443896728\) \(a_{80}=+0.311395946\)
\(a_{81}=+0.111111136\) \(a_{82}=+0.013038242\) \(a_{83}=-0.346650252\) \(a_{84}=+0.186980102\) \(a_{85}=-0.624801063\)
\(a_{86}=+0.248847042\) \(a_{87}=-1.036753841\) \(a_{88}=-0.206001904\) \(a_{89}=+0.774701828\) \(a_{90}=+0.066445814\)
\(a_{91}=+0.130058440\) \(a_{92}=+0.332408344\) \(a_{93}=-0.717076422\) \(a_{94}=-0.461675489\) \(a_{95}=-0.204385948\)
\(a_{96}=-0.534720495\) \(a_{97}=+0.668992128\) \(a_{98}=+0.054050163\) \(a_{99}=+0.097741360\) \(a_{100}=+0.619006242\)

Showing 100 of 1500 available coefficients

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