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: \( 14.1438850658 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.301722520\) \(a_{4}=+0.000000000\) \(a_{5}=+1.451566998\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.110630377\) \(a_{8}=+0.000000000\) \(a_{9}=+0.694481518\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.895164036\) \(a_{12}=+0.000000000\) \(a_{13}=-0.764579790\) \(a_{14}=+0.000000000\) \(a_{15}=+1.889537451\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.421898456\) \(a_{18}=+0.000000000\) \(a_{19}=+1.610304355\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.445732575\) \(a_{22}=+0.000000000\) \(a_{23}=-0.822013006\) \(a_{24}=+0.000000000\) \(a_{25}=+1.107046751\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.397700288\) \(a_{28}=+0.000000000\) \(a_{29}=+1.156110684\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.728097007\) \(a_{32}=+0.000000000\) \(a_{33}=-1.165255184\) \(a_{34}=+0.000000000\) \(a_{35}=+1.612154402\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.373206004\) \(a_{38}=+0.000000000\) \(a_{39}=-0.995270731\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.176917083\) \(a_{42}=+0.000000000\) \(a_{43}=-0.766105861\) \(a_{44}=+0.000000000\) \(a_{45}=+1.008086453\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.098548575\) \(a_{48}=+0.000000000\) \(a_{49}=+0.233499833\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.549194721\) \(a_{52}=+0.000000000\) \(a_{53}=-1.398787800\) \(a_{54}=+0.000000000\) \(a_{55}=-1.299390572\)
\(a_{56}=+0.000000000\) \(a_{57}=+2.096169443\) \(a_{58}=+0.000000000\) \(a_{59}=+1.008082897\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.478693769\) \(a_{62}=+0.000000000\) \(a_{63}=+0.771312273\) \(a_{64}=+0.000000000\) \(a_{65}=-1.109838792\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.652853957\) \(a_{68}=+0.000000000\) \(a_{69}=-1.070032769\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.459239911\) \(a_{72}=+0.000000000\) \(a_{73}=+0.400416467\) \(a_{74}=+0.000000000\) \(a_{75}=+1.441067686\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.994196370\) \(a_{78}=+0.000000000\) \(a_{79}=+0.366067248\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.212176939\) \(a_{82}=+0.000000000\) \(a_{83}=-1.099385802\) \(a_{84}=+0.000000000\) \(a_{85}=+0.612413876\)
\(a_{86}=+0.000000000\) \(a_{87}=+1.504935313\) \(a_{88}=+0.000000000\) \(a_{89}=+0.502152719\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.849165540\) \(a_{92}=+0.000000000\) \(a_{93}=-0.947780270\) \(a_{94}=+0.000000000\) \(a_{95}=+2.337464659\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.256950722\) \(a_{98}=+0.000000000\) \(a_{99}=-0.621674875\) \(a_{100}=+0.000000000\)

Showing 100 of 5000 available coefficients

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