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: \( 9.81303514213 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.826191720\) \(a_{3}=+0.577350269\) \(a_{4}=+2.334976199\) \(a_{5}=-0.490867134\)
\(a_{6}=-1.054352281\) \(a_{7}=-0.377964473\) \(a_{8}=-2.437922481\) \(a_{9}=+0.333333333\) \(a_{10}=+0.896417497\)
\(a_{11}=+1.462392621\) \(a_{12}=+1.348099137\) \(a_{13}=-0.411145447\) \(a_{14}=+0.690235591\) \(a_{15}=-0.283402272\)
\(a_{16}=+2.117137651\) \(a_{17}=+1.205821120\) \(a_{18}=-0.608730573\) \(a_{19}=-0.431454002\) \(a_{20}=-1.146163076\)
\(a_{21}=-0.218217890\) \(a_{22}=-2.670609295\) \(a_{23}=-0.533881547\) \(a_{24}=-1.407535201\) \(a_{25}=-0.759049456\)
\(a_{26}=+0.750830412\) \(a_{27}=+0.192450090\) \(a_{28}=-0.882538049\) \(a_{29}=+1.396652372\) \(a_{30}=+0.517546883\)
\(a_{31}=-1.318031482\) \(a_{32}=-1.428376768\) \(a_{33}=+0.844312773\) \(a_{34}=-2.202060546\) \(a_{35}=+0.185530338\)
\(a_{36}=+0.778325400\) \(a_{37}=+1.367641004\) \(a_{38}=+0.787917726\) \(a_{39}=-0.237374935\) \(a_{40}=+1.196696023\)
\(a_{41}=-1.444557014\) \(a_{42}=+0.398507704\) \(a_{43}=-1.510550641\) \(a_{44}=+3.414651963\) \(a_{45}=-0.163622378\)
\(a_{46}=+0.974970060\) \(a_{47}=+0.091644557\) \(a_{48}=+1.222329993\) \(a_{49}=+0.142857143\) \(a_{50}=+1.386169832\)
\(a_{51}=+0.696181148\) \(a_{52}=-0.960014834\) \(a_{53}=-1.120795925\) \(a_{54}=-0.351450760\) \(a_{55}=-0.717840475\)
\(a_{56}=+0.921448086\) \(a_{57}=-0.249100084\) \(a_{58}=-2.550554998\) \(a_{59}=+0.819139594\) \(a_{60}=-0.661737560\)
\(a_{61}=+1.710826838\) \(a_{62}=+2.406978179\) \(a_{63}=-0.125988158\) \(a_{64}=+0.491352175\) \(a_{65}=+0.201817788\)
\(a_{66}=-1.541876996\) \(a_{67}=+0.404471601\) \(a_{68}=+2.815563616\) \(a_{69}=-0.308236655\) \(a_{70}=-0.338813967\)
\(a_{71}=+1.469791830\) \(a_{72}=-0.812640827\) \(a_{73}=+0.492738648\) \(a_{74}=-2.497574678\) \(a_{75}=-0.438237408\)
\(a_{76}=-1.007434825\) \(a_{77}=-0.552732456\) \(a_{78}=+0.433492140\) \(a_{79}=+0.377908942\) \(a_{80}=-1.039233292\)
\(a_{81}=+0.111111111\) \(a_{82}=+2.638038059\) \(a_{83}=+0.205048792\) \(a_{84}=-0.509533580\) \(a_{85}=-0.591897958\)
\(a_{86}=+2.758555074\) \(a_{87}=+0.806357623\) \(a_{88}=-3.565199846\) \(a_{89}=+1.644479680\) \(a_{90}=+0.298805832\)
\(a_{91}=+0.155398372\) \(a_{92}=-1.246600705\) \(a_{93}=-0.760965831\) \(a_{94}=-0.167360532\) \(a_{95}=+0.211786590\)
\(a_{96}=-0.824673711\) \(a_{97}=+1.096313980\) \(a_{98}=-0.260884531\) \(a_{99}=+0.487464207\) \(a_{100}=-1.772362414\)

Showing 100 of 292 available coefficients

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