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: \( 6.14731585536 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.298102895\) \(a_{3}=-0.577350269\) \(a_{4}=-0.911134664\) \(a_{5}=+1.700920739\)
\(a_{6}=-0.172109786\) \(a_{7}=+0.377964473\) \(a_{8}=-0.569714775\) \(a_{9}=+0.333333333\) \(a_{10}=+0.507049396\)
\(a_{11}=-0.982978644\) \(a_{12}=+0.526043844\) \(a_{13}=-0.810792799\) \(a_{14}=+0.112672303\) \(a_{15}=-0.982027047\)
\(a_{16}=+0.741301041\) \(a_{17}=-1.680733274\) \(a_{18}=+0.099367632\) \(a_{19}=-0.648693335\) \(a_{20}=-1.549767847\)
\(a_{21}=-0.218217890\) \(a_{22}=-0.293028779\) \(a_{23}=+0.418406985\) \(a_{24}=+0.328924979\) \(a_{25}=+1.893131361\)
\(a_{26}=-0.241699680\) \(a_{27}=-0.192450090\) \(a_{28}=-0.344376533\) \(a_{29}=-1.534268677\) \(a_{30}=-0.292745105\)
\(a_{31}=-0.507655606\) \(a_{32}=+0.790698761\) \(a_{33}=+0.567522985\) \(a_{34}=-0.501031454\) \(a_{35}=+0.642887611\)
\(a_{36}=-0.303711555\) \(a_{37}=-0.555102077\) \(a_{38}=-0.193377361\) \(a_{39}=+0.468111441\) \(a_{40}=-0.969039677\)
\(a_{41}=-0.594641648\) \(a_{42}=-0.065051385\) \(a_{43}=-0.575913887\) \(a_{44}=+0.895625917\) \(a_{45}=+0.566973580\)
\(a_{46}=+0.124728333\) \(a_{47}=+1.097041126\) \(a_{48}=-0.427990355\) \(a_{49}=+0.142857143\) \(a_{50}=+0.564347939\)
\(a_{51}=+0.970371808\) \(a_{52}=+0.738741425\) \(a_{53}=-1.159330512\) \(a_{54}=-0.057369929\) \(a_{55}=-1.671968762\)
\(a_{56}=-0.215331945\) \(a_{57}=+0.374523271\) \(a_{58}=-0.457369934\) \(a_{59}=+0.271589267\) \(a_{60}=+0.894758883\)
\(a_{61}=-0.636400033\) \(a_{62}=-0.151333606\) \(a_{63}=+0.125988158\) \(a_{64}=-0.505591451\) \(a_{65}=-1.379094287\)
\(a_{66}=+0.169180245\) \(a_{67}=+0.161667038\) \(a_{68}=+1.531374347\) \(a_{69}=-0.241567385\) \(a_{70}=+0.191646658\)
\(a_{71}=+0.778175870\) \(a_{72}=-0.189904925\) \(a_{73}=-1.396708980\) \(a_{74}=-0.165477536\) \(a_{75}=-1.092999901\)
\(a_{76}=+0.591046984\) \(a_{77}=-0.371531005\) \(a_{78}=+0.139545375\) \(a_{79}=+1.700342385\) \(a_{80}=+1.260894314\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.177264396\) \(a_{83}=+1.186572975\) \(a_{84}=+0.198825884\) \(a_{85}=-2.858794083\)
\(a_{86}=-0.171681597\) \(a_{87}=+0.885810434\) \(a_{88}=+0.560017457\) \(a_{89}=+0.515007390\) \(a_{90}=+0.169016465\)
\(a_{91}=-0.306450873\) \(a_{92}=-0.381225107\) \(a_{93}=+0.293095101\) \(a_{94}=+0.327031135\) \(a_{95}=-1.103375946\)
\(a_{96}=-0.456510143\) \(a_{97}=+1.334623740\) \(a_{98}=+0.042586128\) \(a_{99}=-0.327659548\) \(a_{100}=-1.724897607\)

Showing 100 of 226 available coefficients

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