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: \( 5.88286352614 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.906570859\) \(a_{3}=-0.577350269\) \(a_{4}=-0.178129279\) \(a_{5}=+0.537633621\)
\(a_{6}=-0.523408929\) \(a_{7}=+0.377964473\) \(a_{8}=-1.068057671\) \(a_{9}=+0.333333333\) \(a_{10}=+0.487402973\)
\(a_{11}=+1.638330424\) \(a_{12}=+0.102842987\) \(a_{13}=+1.466557793\) \(a_{14}=+0.342651577\) \(a_{15}=-0.310402916\)
\(a_{16}=-0.790140682\) \(a_{17}=+1.331740171\) \(a_{18}=+0.302190286\) \(a_{19}=-0.868358438\) \(a_{20}=-0.095768289\)
\(a_{21}=-0.218217890\) \(a_{22}=+1.485262619\) \(a_{23}=+1.171688621\) \(a_{24}=+0.616643384\) \(a_{25}=-0.710950090\)
\(a_{26}=+1.329538558\) \(a_{27}=-0.192450090\) \(a_{28}=-0.067326539\) \(a_{29}=-0.759313991\) \(a_{30}=-0.281402238\)
\(a_{31}=-0.609558409\) \(a_{32}=+0.351739155\) \(a_{33}=-0.945890511\) \(a_{34}=+1.207316831\) \(a_{35}=+0.203206408\)
\(a_{36}=-0.059376426\) \(a_{37}=+0.338951832\) \(a_{38}=-0.787228454\) \(a_{39}=-0.846717537\) \(a_{40}=-0.574223713\)
\(a_{41}=+0.841585835\) \(a_{42}=-0.197829980\) \(a_{43}=+1.620874959\) \(a_{44}=-0.291834616\) \(a_{45}=+0.179211207\)
\(a_{46}=+1.062218759\) \(a_{47}=-0.645289241\) \(a_{48}=+0.456187935\) \(a_{49}=+0.142857143\) \(a_{50}=-0.644526633\)
\(a_{51}=-0.768880547\) \(a_{52}=-0.261236882\) \(a_{53}=+0.869070636\) \(a_{54}=-0.174469643\) \(a_{55}=+0.880821518\)
\(a_{56}=-0.403687855\) \(a_{57}=+0.501346978\) \(a_{58}=-0.688371937\) \(a_{59}=-1.337437574\) \(a_{60}=+0.055291847\)
\(a_{61}=+0.058154946\) \(a_{62}=-0.552607890\) \(a_{63}=+0.125988158\) \(a_{64}=+1.109017150\) \(a_{65}=+0.788470776\)
\(a_{66}=-0.857516773\) \(a_{67}=-0.098203146\) \(a_{68}=-0.237221916\) \(a_{69}=-0.676474741\) \(a_{70}=+0.184221008\)
\(a_{71}=+0.182675197\) \(a_{72}=-0.356019224\) \(a_{73}=-0.187069272\) \(a_{74}=+0.307283854\) \(a_{75}=+0.410467226\)
\(a_{76}=+0.154680062\) \(a_{77}=+0.619230695\) \(a_{78}=-0.767609444\) \(a_{79}=+0.404791499\) \(a_{80}=-0.424806196\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.762957193\) \(a_{83}=+0.044540811\) \(a_{84}=+0.038870995\) \(a_{85}=+0.715988290\)
\(a_{86}=+1.469438003\) \(a_{87}=+0.438390137\) \(a_{88}=-1.749831378\) \(a_{89}=-0.315724582\) \(a_{90}=+0.162467658\)
\(a_{91}=+0.554306743\) \(a_{92}=-0.208712049\) \(a_{93}=+0.351928712\) \(a_{94}=-0.585000421\) \(a_{95}=-0.466858691\)
\(a_{96}=-0.203076696\) \(a_{97}=-1.054427892\) \(a_{98}=+0.129510123\) \(a_{99}=+0.546110141\) \(a_{100}=+0.126641027\)

Showing 100 of 238 available coefficients

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