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: \( 1.92464430482 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.337272141\) \(a_{3}=-0.938045923\) \(a_{4}=+0.788296787\) \(a_{5}=-0.265533599\)
\(a_{6}=+1.254422684\) \(a_{7}=+0.377964473\) \(a_{8}=+0.283104807\) \(a_{9}=-1.744813044\) \(a_{10}=+0.355090688\)
\(a_{11}=-0.384729726\) \(a_{12}=-0.739458591\) \(a_{13}=+0.811189439\) \(a_{14}=-0.505441359\) \(a_{15}=+0.249082708\)
\(a_{16}=-1.166884963\) \(a_{17}=-0.421222159\) \(a_{18}=+2.333289885\) \(a_{19}=+0.545018209\) \(a_{20}=-0.209319290\)
\(a_{21}=-0.354548013\) \(a_{22}=+0.514488355\) \(a_{23}=+1.177211086\) \(a_{24}=-0.265565303\) \(a_{25}=-0.929491896\)
\(a_{26}=-1.084781094\) \(a_{27}=-0.447344129\) \(a_{28}=+0.297948286\) \(a_{29}=-0.560794431\) \(a_{30}=-0.333091563\)
\(a_{31}=+0.697949953\) \(a_{32}=+1.277338142\) \(a_{33}=+0.360894068\) \(a_{34}=+0.563288630\) \(a_{35}=-0.100362141\)
\(a_{36}=-1.375430895\) \(a_{37}=-0.566297761\) \(a_{38}=-0.728837760\) \(a_{39}=-0.760933251\) \(a_{40}=-0.075173783\)
\(a_{41}=+1.147308720\) \(a_{42}=+0.474127346\) \(a_{43}=-0.258097529\) \(a_{44}=-0.303281517\) \(a_{45}=+0.463306178\)
\(a_{46}=-1.574251361\) \(a_{47}=+0.833191797\) \(a_{48}=+1.094591904\) \(a_{49}=+0.142855497\) \(a_{50}=+1.242982778\)
\(a_{51}=+0.395125612\) \(a_{52}=+0.639457885\) \(a_{53}=-0.536034049\) \(a_{54}=+0.598221324\) \(a_{55}=+0.102158814\)
\(a_{56}=+0.107003082\) \(a_{57}=-0.511252215\) \(a_{58}=+0.749934612\) \(a_{59}=-1.776895018\) \(a_{60}=+0.196351252\)
\(a_{61}=-0.804794257\) \(a_{62}=-0.933348071\) \(a_{63}=-0.659477376\) \(a_{64}=-0.541264418\) \(a_{65}=-0.215399194\)
\(a_{66}=-0.482613500\) \(a_{67}=+1.274413095\) \(a_{68}=-0.332046962\) \(a_{69}=-1.104277829\) \(a_{70}=+0.134211032\)
\(a_{71}=-0.605210821\) \(a_{72}=-0.493964739\) \(a_{73}=+1.449622836\) \(a_{74}=+0.757294584\) \(a_{75}=+0.871905966\)
\(a_{76}=+0.429635413\) \(a_{77}=-0.145414191\) \(a_{78}=+1.017575072\) \(a_{79}=+0.071701000\) \(a_{80}=+0.309846253\)
\(a_{81}=+1.389619855\) \(a_{82}=-1.534263157\) \(a_{83}=+0.019211246\) \(a_{84}=-0.279489460\) \(a_{85}=+0.111848492\)
\(a_{86}=+0.345146375\) \(a_{87}=+0.526051244\) \(a_{88}=-0.108918406\) \(a_{89}=+0.448398188\) \(a_{90}=-0.619567555\)
\(a_{91}=+0.306600032\) \(a_{92}=+0.927992000\) \(a_{93}=-0.654708270\) \(a_{94}=-1.114201992\) \(a_{95}=-0.144721457\)
\(a_{96}=-1.198202464\) \(a_{97}=-1.480903958\) \(a_{98}=-0.191037820\) \(a_{99}=+0.671280424\) \(a_{100}=-0.732715214\)

Showing 100 of 1500 available coefficients

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