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: \( 4.65900068497 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.819579869\) \(a_{3}=+0.577350269\) \(a_{4}=-0.328288839\) \(a_{5}=-1.616093305\)
\(a_{6}=+0.473184658\) \(a_{7}=-0.377964473\) \(a_{8}=-1.088638792\) \(a_{9}=+0.333333333\) \(a_{10}=-1.324517539\)
\(a_{11}=+0.562099138\) \(a_{12}=-0.189537649\) \(a_{13}=-1.025936447\) \(a_{14}=-0.309772073\) \(a_{15}=-0.933051905\)
\(a_{16}=-0.563937599\) \(a_{17}=+0.292196887\) \(a_{18}=+0.273193289\) \(a_{19}=+1.095212296\) \(a_{20}=+0.530545395\)
\(a_{21}=-0.218217890\) \(a_{22}=+0.460685138\) \(a_{23}=-0.973482376\) \(a_{24}=-0.628525900\) \(a_{25}=+1.611757571\)
\(a_{26}=-0.840836858\) \(a_{27}=+0.192450090\) \(a_{28}=+0.124081517\) \(a_{29}=-0.866913359\) \(a_{30}=-0.764710558\)
\(a_{31}=-1.874241930\) \(a_{32}=+0.626446889\) \(a_{33}=+0.324528088\) \(a_{34}=+0.239478687\) \(a_{35}=+0.610825854\)
\(a_{36}=-0.109429614\) \(a_{37}=+0.495810360\) \(a_{38}=+0.897613948\) \(a_{39}=-0.592324685\) \(a_{40}=+1.759341864\)
\(a_{41}=-0.395214956\) \(a_{42}=-0.178846985\) \(a_{43}=+0.994943391\) \(a_{44}=-0.184530869\) \(a_{45}=-0.538697770\)
\(a_{46}=-0.797846567\) \(a_{47}=-1.789404683\) \(a_{48}=-0.325589532\) \(a_{49}=+0.142857145\) \(a_{50}=+1.320964041\)
\(a_{51}=+0.168699955\) \(a_{52}=+0.336803540\) \(a_{53}=+0.284041669\) \(a_{54}=+0.157728234\) \(a_{55}=-0.908404648\)
\(a_{56}=+0.411466698\) \(a_{57}=+0.632321214\) \(a_{58}=-0.710504771\) \(a_{59}=-1.969270891\) \(a_{60}=+0.306310371\)
\(a_{61}=+0.608672569\) \(a_{62}=-1.536090328\) \(a_{63}=-0.125988699\) \(a_{64}=+1.077361069\) \(a_{65}=+1.658009130\)
\(a_{66}=+0.265976047\) \(a_{67}=-0.482211061\) \(a_{68}=-0.095925004\) \(a_{69}=-0.562040330\) \(a_{70}=+0.500620632\)
\(a_{71}=-0.208613840\) \(a_{72}=-0.362879667\) \(a_{73}=+0.081925677\) \(a_{74}=+0.406356231\) \(a_{75}=+0.930548638\)
\(a_{76}=-0.359545984\) \(a_{77}=-0.212453469\) \(a_{78}=-0.485457436\) \(a_{79}=+1.306422886\) \(a_{80}=+0.911375809\)
\(a_{81}=+0.111111082\) \(a_{82}=-0.323910165\) \(a_{83}=-0.624391206\) \(a_{84}=+0.071638349\) \(a_{85}=-0.472217539\)
\(a_{86}=+0.815435816\) \(a_{87}=-0.500512578\) \(a_{88}=-0.611923069\) \(a_{89}=+0.770168195\) \(a_{90}=-0.441505685\)
\(a_{91}=+0.387767521\) \(a_{92}=+0.319583306\) \(a_{93}=-1.082094118\) \(a_{94}=-1.466560185\) \(a_{95}=-1.769965173\)
\(a_{96}=+0.361679447\) \(a_{97}=+0.468781827\) \(a_{98}=+0.117082620\) \(a_{99}=+0.187366535\) \(a_{100}=-0.529122051\)

Showing 100 of 1500 available coefficients

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