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: \( 3.62224302475 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.690202695\) \(a_{3}=+0.577350269\) \(a_{4}=+1.856785149\) \(a_{5}=+0.125256479\)
\(a_{6}=+0.975838981\) \(a_{7}=-0.377964473\) \(a_{8}=+1.448140568\) \(a_{9}=+0.333333333\) \(a_{10}=+0.211708838\)
\(a_{11}=-1.793094455\) \(a_{12}=+1.072015406\) \(a_{13}=-0.574422956\) \(a_{14}=-0.638836571\) \(a_{15}=+0.072316862\)
\(a_{16}=+0.590865941\) \(a_{17}=+1.029844815\) \(a_{18}=+0.563400898\) \(a_{19}=+1.664116015\) \(a_{20}=+0.232574370\)
\(a_{21}=-0.218217890\) \(a_{22}=-3.030693079\) \(a_{23}=+0.359502158\) \(a_{24}=+0.836084347\) \(a_{25}=-0.984310814\)
\(a_{26}=-0.970891228\) \(a_{27}=+0.192450090\) \(a_{28}=-0.701798821\) \(a_{29}=+1.108971000\) \(a_{30}=+0.122230155\)
\(a_{31}=-0.087579434\) \(a_{32}=-0.449457362\) \(a_{33}=-1.035243566\) \(a_{34}=+1.740646481\) \(a_{35}=-0.047342499\)
\(a_{36}=+0.618928383\) \(a_{37}=+0.145526158\) \(a_{38}=+2.812693372\) \(a_{39}=-0.331643248\) \(a_{40}=+0.181388989\)
\(a_{41}=+0.123604499\) \(a_{42}=-0.368832466\) \(a_{43}=-0.860417481\) \(a_{44}=-3.329391155\) \(a_{45}=+0.041752158\)
\(a_{46}=+0.607631514\) \(a_{47}=+0.203248932\) \(a_{48}=+0.341136615\) \(a_{49}=+0.142857137\) \(a_{50}=-1.663684802\)
\(a_{51}=+0.594581193\) \(a_{52}=-1.066579983\) \(a_{53}=+1.451289696\) \(a_{54}=+0.325279600\) \(a_{55}=-0.224596712\)
\(a_{56}=-0.547345687\) \(a_{57}=+0.960777836\) \(a_{58}=+1.874385776\) \(a_{59}=+0.819291250\) \(a_{60}=+0.134276869\)
\(a_{61}=-1.526061929\) \(a_{62}=-0.148026991\) \(a_{63}=-0.125988167\) \(a_{64}=-1.350539997\) \(a_{65}=-0.071950187\)
\(a_{66}=-1.749771445\) \(a_{67}=-0.068634188\) \(a_{68}=+1.912200546\) \(a_{69}=+0.207558673\) \(a_{70}=-0.080018413\)
\(a_{71}=-0.715022660\) \(a_{72}=+0.482713472\) \(a_{73}=+0.476807852\) \(a_{74}=+0.245968765\) \(a_{75}=-0.568292117\)
\(a_{76}=+3.089905909\) \(a_{77}=+0.677726013\) \(a_{78}=-0.560544301\) \(a_{79}=-0.431942068\) \(a_{80}=+0.074009796\)
\(a_{81}=+0.111111110\) \(a_{82}=+0.208916615\) \(a_{83}=-0.800502703\) \(a_{84}=-0.405183743\) \(a_{85}=+0.128994802\)
\(a_{86}=-1.454279958\) \(a_{87}=+0.640264729\) \(a_{88}=-2.596652817\) \(a_{89}=-0.166297346\) \(a_{90}=+0.070569628\)
\(a_{91}=+0.217111476\) \(a_{92}=+0.667518275\) \(a_{93}=-0.050564102\) \(a_{94}=+0.343531886\) \(a_{95}=+0.208441260\)
\(a_{96}=-0.259494286\) \(a_{97}=-0.191572697\) \(a_{98}=+0.241457582\) \(a_{99}=-0.597698135\) \(a_{100}=-1.827653736\)

Showing 100 of 1500 available coefficients

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