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: \( 4.48238693354 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.069192882\) \(a_{3}=-0.577350269\) \(a_{4}=-0.995212345\) \(a_{5}=+1.595765196\)
\(a_{6}=+0.039948529\) \(a_{7}=-0.377964473\) \(a_{8}=+0.138054492\) \(a_{9}=+0.333333333\) \(a_{10}=-0.110415593\)
\(a_{11}=+1.977068725\) \(a_{12}=+0.574586115\) \(a_{13}=-0.218338521\) \(a_{14}=+0.026152451\) \(a_{15}=-0.921315465\)
\(a_{16}=+0.985659957\) \(a_{17}=+0.246893297\) \(a_{18}=-0.023064294\) \(a_{19}=+0.434141240\) \(a_{20}=-1.588125222\)
\(a_{21}=+0.218217890\) \(a_{22}=-0.136799083\) \(a_{23}=-0.697617682\) \(a_{24}=-0.079705798\) \(a_{25}=+1.546466559\)
\(a_{26}=+0.015107471\) \(a_{27}=-0.192450090\) \(a_{28}=+0.376154910\) \(a_{29}=+1.089404882\) \(a_{30}=+0.063748472\)
\(a_{31}=+0.343461391\) \(a_{32}=-0.206255145\) \(a_{33}=-1.141461160\) \(a_{34}=-0.017083259\) \(a_{35}=-0.603142551\)
\(a_{36}=-0.331737448\) \(a_{37}=+0.724625991\) \(a_{38}=-0.030039483\) \(a_{39}=+0.126057804\) \(a_{40}=+0.220302553\)
\(a_{41}=+1.124531536\) \(a_{42}=-0.015099124\) \(a_{43}=-1.605019682\) \(a_{44}=-1.967603204\) \(a_{45}=+0.531921730\)
\(a_{46}=+0.048270180\) \(a_{47}=+0.713924737\) \(a_{48}=-0.569071043\) \(a_{49}=+0.142857136\) \(a_{50}=-0.107004480\)
\(a_{51}=-0.142543902\) \(a_{52}=+0.217293200\) \(a_{53}=+0.619790878\) \(a_{54}=+0.013316156\) \(a_{55}=+3.154937466\)
\(a_{56}=-0.052179653\) \(a_{57}=-0.250651550\) \(a_{58}=-0.075379124\) \(a_{59}=-1.004793534\) \(a_{60}=+0.916904591\)
\(a_{61}=-0.805956360\) \(a_{62}=-0.023765120\) \(a_{63}=-0.125988375\) \(a_{64}=-0.971388638\) \(a_{65}=-0.348416681\)
\(a_{66}=+0.078981291\) \(a_{67}=-0.059464682\) \(a_{68}=-0.245711258\) \(a_{69}=+0.402769756\) \(a_{70}=+0.041733171\)
\(a_{71}=-0.366773706\) \(a_{72}=+0.046018164\) \(a_{73}=+0.630354034\) \(a_{74}=-0.050138961\) \(a_{75}=-0.892852884\)
\(a_{76}=-0.432062721\) \(a_{77}=-0.747261738\) \(a_{78}=-0.008722303\) \(a_{79}=-0.668821647\) \(a_{80}=+1.572881853\)
\(a_{81}=+0.111111109\) \(a_{82}=-0.077809579\) \(a_{83}=+0.761528119\) \(a_{84}=-0.217173138\) \(a_{85}=+0.393983732\)
\(a_{86}=+0.111055941\) \(a_{87}=-0.628968211\) \(a_{88}=+0.272943225\) \(a_{89}=-0.062359487\) \(a_{90}=-0.036805207\)
\(a_{91}=+0.082524182\) \(a_{92}=+0.694277747\) \(a_{93}=-0.198297457\) \(a_{94}=-0.049398447\) \(a_{95}=+0.692787669\)
\(a_{96}=+0.119081427\) \(a_{97}=+0.774647710\) \(a_{98}=-0.009885584\) \(a_{99}=+0.659023257\) \(a_{100}=-1.539062612\)

Showing 100 of 1500 available coefficients

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