Properties

Label 11.58
Level $11$
Weight $0$
Character 11.1
Symmetry even
\(R\) 9.226402
Fricke sign $-1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(9.22640277044793374436943012276 \pm 6 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.77968923 \pm 1 \cdot 10^{-8} \) \(a_{3}= -1.65621401 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.39208470 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.01817320 \pm 1 \cdot 10^{-8} \) \(a_{6}= +1.29133223 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.49861412 \pm 1 \cdot 10^{-8} \) \(a_{8}= +1.08539345 \pm 1 \cdot 10^{-8} \) \(a_{9}= +1.74304484 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.01416945 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +0.64937617 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +1.09793050 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.38876406 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.03009870 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.45418489 \pm 1 \cdot 10^{-8} \) \(a_{17}= -1.03231354 \pm 1 \cdot 10^{-8} \) \(a_{18}= -1.35903330 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.81700415 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.00712543 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.82581169 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.23508515 \pm 1.1 \cdot 10^{-8} \) \(a_{23}= +1.41882221 \pm 1 \cdot 10^{-8} \) \(a_{24}= -1.79764384 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.99966973 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.85604459 \pm 1 \cdot 10^{-8} \) \(a_{27}= -1.23064128 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.19549897 \pm 1 \cdot 10^{-8} \) \(a_{29}= +1.28247641 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.02346763 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.05249040 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.73127038 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.49936731 \pm 1.1 \cdot 10^{-8} \)
\(a_{34}= +0.80488375 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.00906141 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.68342121 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.99628271 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.63700934 \pm 1 \cdot 10^{-8} \) \(a_{39}= -1.81840787 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.01972507 \pm 1 \cdot 10^{-8} \) \(a_{41}= +1.83052949 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.64387648 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.94170151 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.11821798 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= +0.03167670 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -1.10624040 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.04480637 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.75222738 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.75138396 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.77943173 \pm 1 \cdot 10^{-8} \) \(a_{51}= +1.70973214 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.43048175 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.85818343 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.95951775 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.00547943 \pm 1.1 \cdot 10^{-8} \) \(a_{56}= -0.54119250 \pm 1 \cdot 10^{-8} \) \(a_{57}= +1.35313372 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.99993305 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.94159054 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.01180124 \pm 1 \cdot 10^{-8} \)

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