Properties

Level $28$
Weight $0$
Character 28.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 28 = 2^{2} \cdot 7 \)
Weight: \( 0 \)
Character: 28.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 8.54015343032 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.844817767\) \(a_{4}=+0.000000000\) \(a_{5}=-0.220363011\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.377964473\) \(a_{8}=+0.000000000\) \(a_{9}=+2.403352593\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.859302814\) \(a_{12}=+0.000000000\) \(a_{13}=-1.723360236\) \(a_{14}=+0.000000000\) \(a_{15}=-0.406529599\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.175700463\) \(a_{18}=+0.000000000\) \(a_{19}=+0.229953406\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.697275575\) \(a_{22}=+0.000000000\) \(a_{23}=-0.240323973\) \(a_{24}=+0.000000000\) \(a_{25}=-0.951440143\)
\(a_{26}=+0.000000000\) \(a_{27}=+2.588929797\) \(a_{28}=+0.000000000\) \(a_{29}=+0.740958561\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.285226716\) \(a_{32}=+0.000000000\) \(a_{33}=-3.430074865\) \(a_{34}=+0.000000000\) \(a_{35}=+0.083289390\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.534209420\) \(a_{38}=+0.000000000\) \(a_{39}=-3.179285581\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.815374972\) \(a_{42}=+0.000000000\) \(a_{43}=-0.495878034\) \(a_{44}=+0.000000000\) \(a_{45}=-0.529610015\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.330631265\) \(a_{48}=+0.000000000\) \(a_{49}=+0.142857143\) \(a_{50}=+0.000000000\)
\(a_{51}=-2.168953103\) \(a_{52}=+0.000000000\) \(a_{53}=-0.909450088\) \(a_{54}=+0.000000000\) \(a_{55}=+0.409721567\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.424222130\) \(a_{58}=+0.000000000\) \(a_{59}=+0.143918420\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.159244504\) \(a_{62}=+0.000000000\) \(a_{63}=-0.908381896\) \(a_{64}=+0.000000000\) \(a_{65}=+0.379764851\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.789388265\) \(a_{68}=+0.000000000\) \(a_{69}=-0.443353934\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.011137482\) \(a_{72}=+0.000000000\) \(a_{73}=-0.256101117\) \(a_{74}=+0.000000000\) \(a_{75}=-1.755233680\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.702750408\) \(a_{78}=+0.000000000\) \(a_{79}=+0.864364238\) \(a_{80}=+0.000000000\)
\(a_{81}=+2.372751094\) \(a_{82}=+0.000000000\) \(a_{83}=-1.087253213\) \(a_{84}=+0.000000000\) \(a_{85}=+0.259080895\)
\(a_{86}=+0.000000000\) \(a_{87}=+1.366933518\) \(a_{88}=+0.000000000\) \(a_{89}=-0.892021094\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.651368943\) \(a_{92}=+0.000000000\) \(a_{93}=+0.526191313\) \(a_{94}=+0.000000000\) \(a_{95}=-0.050673225\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.280139863\) \(a_{98}=+0.000000000\) \(a_{99}=-4.468560239\) \(a_{100}=+0.000000000\)

Showing 100 of 372 available coefficients

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