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: \( 4.99569969205 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.580816516\) \(a_{3}=-0.577350269\) \(a_{4}=+1.498980858\) \(a_{5}=+0.672840659\)
\(a_{6}=+0.912684841\) \(a_{7}=-0.377964473\) \(a_{8}=-0.788797182\) \(a_{9}=+0.333333333\) \(a_{10}=-1.063637627\)
\(a_{11}=+0.650303520\) \(a_{12}=-0.865437002\) \(a_{13}=+0.160912803\) \(a_{14}=+0.597492481\) \(a_{15}=-0.388464736\)
\(a_{16}=-0.252037245\) \(a_{17}=-0.182724074\) \(a_{18}=-0.526938839\) \(a_{19}=-1.770327029\) \(a_{20}=+1.008575269\)
\(a_{21}=+0.218217890\) \(a_{22}=-1.028010545\) \(a_{23}=+1.739978038\) \(a_{24}=+0.455412265\) \(a_{25}=-0.547285447\)
\(a_{26}=-0.254373617\) \(a_{27}=-0.192450090\) \(a_{28}=-0.566561510\) \(a_{29}=-1.608100842\) \(a_{30}=+0.614091470\)
\(a_{31}=+0.509506796\) \(a_{32}=+1.187221822\) \(a_{33}=-0.375452912\) \(a_{34}=+0.288853234\) \(a_{35}=-0.254309865\)
\(a_{36}=+0.499660286\) \(a_{37}=-0.227293628\) \(a_{38}=+2.798562207\) \(a_{39}=-0.092903050\) \(a_{40}=-0.530734816\)
\(a_{41}=-1.756748227\) \(a_{42}=-0.344962445\) \(a_{43}=-1.674424599\) \(a_{44}=+0.974792529\) \(a_{45}=+0.224280220\)
\(a_{46}=-2.750586021\) \(a_{47}=+0.503056146\) \(a_{48}=+0.145513771\) \(a_{49}=+0.142857143\) \(a_{50}=+0.865157874\)
\(a_{51}=+0.105495793\) \(a_{52}=+0.241205212\) \(a_{53}=-0.726607545\) \(a_{54}=+0.304228281\) \(a_{55}=+0.437550649\)
\(a_{56}=+0.298137311\) \(a_{57}=+1.022098787\) \(a_{58}=+2.542112370\) \(a_{59}=-0.430390805\) \(a_{60}=-0.582301202\)
\(a_{61}=+0.853739228\) \(a_{62}=-0.805436759\) \(a_{63}=-0.125988157\) \(a_{64}=-1.624742612\) \(a_{65}=+0.108268674\)
\(a_{66}=+0.593522166\) \(a_{67}=+0.484815902\) \(a_{68}=-0.273899900\) \(a_{69}=-1.004576790\) \(a_{70}=+0.402017245\)
\(a_{71}=-0.545634275\) \(a_{72}=-0.262932394\) \(a_{73}=-0.683250627\) \(a_{74}=+0.359309522\) \(a_{75}=+0.315975400\)
\(a_{76}=-2.653686331\) \(a_{77}=-0.245791626\) \(a_{78}=+0.146862676\) \(a_{79}=-0.434694309\) \(a_{80}=-0.169580906\)
\(a_{81}=+0.111111109\) \(a_{82}=+2.777096611\) \(a_{83}=-0.272329266\) \(a_{84}=+0.327104443\) \(a_{85}=-0.122944191\)
\(a_{86}=+2.646958065\) \(a_{87}=+0.928437455\) \(a_{88}=-0.512957594\) \(a_{89}=-1.515092480\) \(a_{90}=-0.354545867\)
\(a_{91}=-0.060819334\) \(a_{92}=+2.608193783\) \(a_{93}=-0.294163888\) \(a_{94}=-0.795239476\) \(a_{95}=-1.191147980\)
\(a_{96}=-0.685442820\) \(a_{97}=-0.301621794\) \(a_{98}=-0.225830834\) \(a_{99}=+0.216767917\) \(a_{100}=-0.820370455\)

Showing 100 of 1500 available coefficients

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