Properties

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

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Maass form invariants

Level: \( 28 = 2^{2} \cdot 7 \)
Weight: \( 0 \)
Character: 28.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.816781268055 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.285284121\) \(a_{4}=+0.000000000\) \(a_{5}=-0.625338483\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.377964473\) \(a_{8}=+0.000000000\) \(a_{9}=-0.918612970\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.941580813\) \(a_{12}=+0.000000000\) \(a_{13}=+1.074442953\) \(a_{14}=+0.000000000\) \(a_{15}=-0.178399139\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.799619181\) \(a_{18}=+0.000000000\) \(a_{19}=-0.419814678\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.107827262\) \(a_{22}=+0.000000000\) \(a_{23}=-0.418374175\) \(a_{24}=+0.000000000\) \(a_{25}=-0.608951782\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.547349814\) \(a_{28}=+0.000000000\) \(a_{29}=+0.285627396\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.003307401\) \(a_{32}=+0.000000000\) \(a_{33}=+0.268618054\) \(a_{34}=+0.000000000\) \(a_{35}=+0.236355730\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.470646477\) \(a_{38}=+0.000000000\) \(a_{39}=+0.306521513\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.368882583\) \(a_{42}=+0.000000000\) \(a_{43}=+1.037681728\) \(a_{44}=+0.000000000\) \(a_{45}=+0.574444042\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.802763432\) \(a_{48}=+0.000000000\) \(a_{49}=+0.142857144\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.228118654\) \(a_{52}=+0.000000000\) \(a_{53}=-1.411848547\) \(a_{54}=+0.000000000\) \(a_{55}=-0.588806715\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.119766466\) \(a_{58}=+0.000000000\) \(a_{59}=-0.880530213\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.416648207\) \(a_{62}=+0.000000000\) \(a_{63}=+0.347180866\) \(a_{64}=+0.000000000\) \(a_{65}=-0.671809171\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.464472555\) \(a_{68}=+0.000000000\) \(a_{69}=-0.119387769\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.116289427\) \(a_{72}=+0.000000000\) \(a_{73}=+0.793375014\) \(a_{74}=+0.000000000\) \(a_{75}=-0.173233418\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.355437352\) \(a_{78}=+0.000000000\) \(a_{79}=+0.331182628\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.765710394\) \(a_{82}=+0.000000000\) \(a_{83}=+1.144127594\) \(a_{84}=+0.000000000\) \(a_{85}=-0.500041843\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.081505541\) \(a_{88}=+0.000000000\) \(a_{89}=+0.792892028\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.404695479\) \(a_{92}=+0.000000000\) \(a_{93}=-0.285961663\) \(a_{94}=+0.000000000\) \(a_{95}=+0.262612009\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.121405444\) \(a_{98}=+0.000000000\) \(a_{99}=-0.867520468\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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