Properties

Label 11.133
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 13.54217
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(13.5421737879709685184071760475 \pm 10 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.40646650 \pm 3.3 \cdot 10^{-5} \) \(a_{3}= -1.84127746 \pm 2.7 \cdot 10^{-5} \)
\(a_{4}= -0.83478498 \pm 3.9 \cdot 10^{-5} \) \(a_{5}= -1.48852194 \pm 2.8 \cdot 10^{-5} \) \(a_{6}= -0.74841761 \pm 3.4 \cdot 10^{-5} \)
\(a_{7}= +0.80165017 \pm 2.8 \cdot 10^{-5} \) \(a_{8}= -0.74577863 \pm 3.3 \cdot 10^{-5} \) \(a_{9}= +2.39030267 \pm 3.1 \cdot 10^{-5} \)
\(a_{10}= -0.60503431 \pm 3.5 \cdot 10^{-5} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +1.53707077 \pm 3.6 \cdot 10^{-5} \)
\(a_{13}= +1.03237429 \pm 2.2 \cdot 10^{-5} \) \(a_{14}= +0.32584394 \pm 2.4 \cdot 10^{-5} \) \(a_{15}= +2.74078189 \pm 2.1 \cdot 10^{-5} \)
\(a_{16}= +0.53165095 \pm 2.9 \cdot 10^{-5} \) \(a_{17}= +0.00058707 \pm 2.8 \cdot 10^{-5} \) \(a_{18}= +0.97157797 \pm 3.1 \cdot 10^{-5} \)
\(a_{19}= -1.06133060 \pm 2.0 \cdot 10^{-5} \) \(a_{20}= +1.24259576 \pm 3.8 \cdot 10^{-5} \) \(a_{21}= -1.47606038 \pm 2.2 \cdot 10^{-5} \)
\(a_{22}= -0.12255426 \pm 3.3 \cdot 10^{-5} \) \(a_{23}= -0.97369245 \pm 2.6 \cdot 10^{-5} \) \(a_{24}= +1.37318539 \pm 3.8 \cdot 10^{-5} \)
\(a_{25}= +1.21569756 \pm 2.3 \cdot 10^{-5} \) \(a_{26}= +0.41962557 \pm 1.7 \cdot 10^{-5} \) \(a_{27}= -2.55993296 \pm 2.6 \cdot 10^{-5} \)
\(a_{28}= -0.66920552 \pm 2.9 \cdot 10^{-5} \) \(a_{29}= +0.92384540 \pm 2.6 \cdot 10^{-5} \) \(a_{30}= +1.11403603 \pm 2.0 \cdot 10^{-5} \)
\(a_{31}= +0.82574695 \pm 2.8 \cdot 10^{-5} \) \(a_{32}= +0.96187694 \pm 2.4 \cdot 10^{-5} \) \(a_{33}= +0.55516604 \pm 2.7 \cdot 10^{-5} \)
\(a_{34}= +0.00023862 \pm 3.4 \cdot 10^{-5} \) \(a_{35}= -1.19327386 \pm 2.7 \cdot 10^{-5} \) \(a_{36}= -1.99538877 \pm 3.2 \cdot 10^{-5} \)
\(a_{37}= +0.19738509 \pm 2.8 \cdot 10^{-5} \) \(a_{38}= -0.43139534 \pm 2.8 \cdot 10^{-5} \) \(a_{39}= -1.90088751 \pm 1.6 \cdot 10^{-5} \)
\(a_{40}= +1.11010786 \pm 2.7 \cdot 10^{-5} \) \(a_{41}= +0.69961162 \pm 1.8 \cdot 10^{-5} \) \(a_{42}= -0.59996910 \pm 2.4 \cdot 10^{-5} \)
\(a_{43}= +0.66129722 \pm 2.7 \cdot 10^{-5} \) \(a_{44}= +0.25169714 \pm 3.9 \cdot 10^{-5} \) \(a_{45}= -3.55801797 \pm 3.0 \cdot 10^{-5} \)
\(a_{46}= -0.39577337 \pm 3.8 \cdot 10^{-5} \) \(a_{47}= +1.30289297 \pm 2.2 \cdot 10^{-5} \) \(a_{48}= -0.97891691 \pm 3.0 \cdot 10^{-5} \)
\(a_{49}= -0.35735701 \pm 2.5 \cdot 10^{-5} \) \(a_{50}= +0.49414034 \pm 3.6 \cdot 10^{-5} \) \(a_{51}= -0.00108095 \pm 2.8 \cdot 10^{-5} \)
\(a_{52}= -0.86181055 \pm 2.4 \cdot 10^{-5} \) \(a_{53}= -1.20943553 \pm 2.2 \cdot 10^{-5} \) \(a_{54}= -1.04052700 \pm 2.2 \cdot 10^{-5} \)
\(a_{55}= +0.44880625 \pm 2.8 \cdot 10^{-5} \) \(a_{56}= -0.59785357 \pm 1.9 \cdot 10^{-5} \) \(a_{57}= +1.95420411 \pm 1.8 \cdot 10^{-5} \)
\(a_{58}= +0.37551221 \pm 2.5 \cdot 10^{-5} \) \(a_{59}= -1.53744290 \pm 3.2 \cdot 10^{-5} \) \(a_{60}= -2.28796356 \pm 1.7 \cdot 10^{-5} \)

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