Properties

Label 15.4
Level $15$
Weight $0$
Character 15.1
Symmetry odd
\(R\) 2.361334
Fricke sign $+1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(2.36133422204256634651088038989 \pm 6 \cdot 10^{-12}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= -1.64178940 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.69547245 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.94788755 \pm 1.7 \cdot 10^{-8} \)
\(a_{7}= -1.04966898 \pm 1 \cdot 10^{-8} \) \(a_{8}= -1.14181930 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.73423054 \pm 1.7 \cdot 10^{-8} \) \(a_{11}= -0.89220513 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.97888147 \pm 1.7 \cdot 10^{-8} \)
\(a_{13}= +0.77857875 \pm 1 \cdot 10^{-8} \) \(a_{14}= +1.72333541 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.17915438 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.32543838 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.54726313 \pm 1.7 \cdot 10^{-8} \)
\(a_{19}= -1.12662383 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.75823833 \pm 1.7 \cdot 10^{-8} \) \(a_{21}= +0.60602667 \pm 1.6 \cdot 10^{-8} \)
\(a_{22}= +1.46481293 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.07082860 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.65922968 \pm 1.5 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -1.27826235 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -1.77968483 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.66390839 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.42390820 \pm 1.7 \cdot 10^{-8} \)
\(a_{31}= -0.26865011 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.84768554 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.51511487 \pm 1.7 \cdot 10^{-8} \)
\(a_{34}= +0.53430128 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.46942624 \pm 1.6 \cdot 10^{-8} \) \(a_{36}= +0.56515748 \pm 1.7 \cdot 10^{-8} \)
\(a_{37}= -0.70880633 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.84967907 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.44951265 \pm 1.6 \cdot 10^{-8} \)
\(a_{40}= +0.51063711 \pm 1.5 \cdot 10^{-8} \) \(a_{41}= -0.32393351 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.99496816 \pm 2.4 \cdot 10^{-8} \)
\(a_{43}= +0.42282142 \pm 1 \cdot 10^{-8} \) \(a_{44}= -1.51270922 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +0.11628564 \pm 1 \cdot 10^{-8} \) \(a_{47}= -1.70489639 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.10343483 \pm 1.6 \cdot 10^{-8} \)
\(a_{49}= +0.10180496 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.32835788 \pm 1.7 \cdot 10^{-8} \) \(a_{51}= +0.18789194 \pm 1.6 \cdot 10^{-8} \)
\(a_{52}= +1.32005883 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.22510293 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.31596252 \pm 1.7 \cdot 10^{-8} \)
\(a_{55}= +0.39900626 \pm 1.7 \cdot 10^{-8} \) \(a_{56}= +1.19853230 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.65045657 \pm 1.6 \cdot 10^{-8} \)
\(a_{58}= -1.08999775 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.76501444 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.43776910 \pm 1.7 \cdot 10^{-8} \)

Displaying $a_n$ with $n$ up to: 60 180 1000