Properties

Label 15.5
Level $15$
Weight $0$
Character 15.1
Symmetry even
\(R\) 2.916537
Fricke sign $+1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(2.91653733402465304220481312243 \pm 8 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.90058800 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.18894125 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.51995472 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +0.85289474 \pm 1 \cdot 10^{-8} \) \(a_{8}= -1.07074623 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.40275520 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -1.29144452 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.10908528 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= -0.28728083 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.76810677 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -0.77535995 \pm 1 \cdot 10^{-8} \) \(a_{17}= +1.02957169 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.30019600 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= +1.11698316 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.08449710 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= +0.49241901 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -1.16305944 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.30935321 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.61819562 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -0.25872167 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.16114700 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.46725426 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.23253082 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +1.67377119 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.37246636 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.74561584 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.92721991 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.38142612 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -0.06298042 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= -1.20404678 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.00594163 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.16586167 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= -0.47885227 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -1.13752350 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.44346665 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.81315051 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.24400715 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= -1.17918779 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.18114045 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.44765428 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= -0.27257056 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.18011760 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= +0.59442349 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= +0.05427920 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.37673931 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.17331824 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= -0.57755155 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= -0.91323382 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.64489053 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= -0.42080358 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.19442356 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.04878442 \pm 1.0 \cdot 10^{-8} \)

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