Properties

Level $4$
Weight $0$
Character 4.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 4 = 2^{2} \)
Weight: \( 0 \)
Character: 4.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 13.228828713 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.701988550\) \(a_{4}=+0.000000000\) \(a_{5}=-1.198818837\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.186007369\) \(a_{8}=+0.000000000\) \(a_{9}=-0.507212076\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.025580760\) \(a_{12}=+0.000000000\) \(a_{13}=+1.813805891\) \(a_{14}=+0.000000000\) \(a_{15}=+0.841557097\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.141229477\) \(a_{18}=+0.000000000\) \(a_{19}=+1.281839313\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.130575043\) \(a_{22}=+0.000000000\) \(a_{23}=-0.132069762\) \(a_{24}=+0.000000000\) \(a_{25}=+0.437166604\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.058045619\) \(a_{28}=+0.000000000\) \(a_{29}=-1.583532811\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.210984149\) \(a_{32}=+0.000000000\) \(a_{33}=+0.719945950\) \(a_{34}=+0.000000000\) \(a_{35}=-0.222989137\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.720847555\) \(a_{38}=+0.000000000\) \(a_{39}=-1.273270967\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.123870921\) \(a_{42}=+0.000000000\) \(a_{43}=+0.436314008\) \(a_{44}=+0.000000000\) \(a_{45}=+0.608055391\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.527544528\) \(a_{48}=+0.000000000\) \(a_{49}=-0.965401259\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.801130025\) \(a_{52}=+0.000000000\) \(a_{53}=+0.136071790\) \(a_{54}=+0.000000000\) \(a_{55}=+1.229485534\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.899836520\) \(a_{58}=+0.000000000\) \(a_{59}=+1.149780631\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.227406711\) \(a_{62}=+0.000000000\) \(a_{63}=-0.094345184\) \(a_{64}=+0.000000000\) \(a_{65}=-2.174424667\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.357848064\) \(a_{68}=+0.000000000\) \(a_{69}=+0.092711458\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.790963816\) \(a_{72}=+0.000000000\) \(a_{73}=+0.274080251\) \(a_{74}=+0.000000000\) \(a_{75}=-0.306885950\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.190765579\) \(a_{78}=+0.000000000\) \(a_{79}=-1.090894286\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.235523834\) \(a_{82}=+0.000000000\) \(a_{83}=+1.394640723\) \(a_{84}=+0.000000000\) \(a_{85}=-1.368127394\)
\(a_{86}=+0.000000000\) \(a_{87}=+1.111621901\) \(a_{88}=+0.000000000\) \(a_{89}=+0.671790955\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.337381261\) \(a_{92}=+0.000000000\) \(a_{93}=-0.148108457\) \(a_{94}=+0.000000000\) \(a_{95}=-1.536693114\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.837291192\) \(a_{98}=+0.000000000\) \(a_{99}=+0.520186946\) \(a_{100}=+0.000000000\)

Showing 100 of 5000 available coefficients

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