Properties

Label 10.49
Level $10$
Weight $0$
Character 10.1
Symmetry odd
\(R\) 12.01500
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(12.0150070406973263972274387053 \pm 7 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -1.50507564 \pm 1.2 \cdot 10^{-6} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +1.06424919 \pm 1.3 \cdot 10^{-6} \)
\(a_{7}= -1.56407173 \pm 1.6 \cdot 10^{-6} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +1.26525268 \pm 1.3 \cdot 10^{-6} \)
\(a_{10}= +0.31622777 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +1.24295679 \pm 1.2 \cdot 10^{-6} \) \(a_{12}= -0.75253782 \pm 1.3 \cdot 10^{-6} \)
\(a_{13}= +0.02181166 \pm 1.4 \cdot 10^{-6} \) \(a_{14}= +1.10596573 \pm 1.6 \cdot 10^{-6} \) \(a_{15}= +0.67309029 \pm 1.3 \cdot 10^{-6} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.77510394 \pm 8.5 \cdot 10^{-7} \) \(a_{18}= -0.89466875 \pm 1.4 \cdot 10^{-6} \)
\(a_{19}= +1.54966375 \pm 1.1 \cdot 10^{-6} \) \(a_{20}= -0.22360680 \pm 8.4 \cdot 10^{-8} \) \(a_{21}= +2.35404626 \pm 1.3 \cdot 10^{-6} \)
\(a_{22}= -0.87890318 \pm 1.2 \cdot 10^{-6} \) \(a_{23}= -0.82473372 \pm 1.9 \cdot 10^{-6} \) \(a_{24}= +0.53212460 \pm 1.3 \cdot 10^{-6} \)
\(a_{25}= +0.2 \) \(a_{26}= -0.01542317 \pm 1.4 \cdot 10^{-6} \) \(a_{27}= -0.39922534 \pm 1.5 \cdot 10^{-6} \)
\(a_{28}= -0.78203587 \pm 1.6 \cdot 10^{-6} \) \(a_{29}= -1.40588731 \pm 2.0 \cdot 10^{-6} \) \(a_{30}= -0.47594671 \pm 1.3 \cdot 10^{-6} \)
\(a_{31}= +0.53244342 \pm 1.1 \cdot 10^{-6} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -1.87074399 \pm 1.0 \cdot 10^{-6} \)
\(a_{34}= -0.54808125 \pm 8.6 \cdot 10^{-7} \) \(a_{35}= +0.69947414 \pm 1.6 \cdot 10^{-6} \) \(a_{36}= +0.63262634 \pm 1.4 \cdot 10^{-6} \)
\(a_{37}= +0.02700126 \pm 1.5 \cdot 10^{-6} \) \(a_{38}= -1.09577775 \pm 1.1 \cdot 10^{-6} \) \(a_{39}= -0.03282820 \pm 1.1 \cdot 10^{-6} \)
\(a_{40}= +0.15811388 \pm 1.2 \cdot 10^{-7} \) \(a_{41}= -1.39122423 \pm 1.0 \cdot 10^{-6} \) \(a_{42}= -1.66456208 \pm 2.9 \cdot 10^{-6} \)
\(a_{43}= +0.85144628 \pm 1.3 \cdot 10^{-6} \) \(a_{44}= +0.62147840 \pm 1.2 \cdot 10^{-6} \) \(a_{45}= -0.56583820 \pm 1.4 \cdot 10^{-6} \)
\(a_{46}= +0.58317481 \pm 1.9 \cdot 10^{-6} \) \(a_{47}= -0.66849687 \pm 1.0 \cdot 10^{-6} \) \(a_{48}= -0.37626891 \pm 1.3 \cdot 10^{-6} \)
\(a_{49}= +1.44632039 \pm 1.6 \cdot 10^{-6} \) \(a_{50}= -0.14142136 \pm 1.5 \cdot 10^{-7} \) \(a_{51}= -1.16659005 \pm 1.0 \cdot 10^{-6} \)
\(a_{52}= +0.01090583 \pm 1.4 \cdot 10^{-6} \) \(a_{53}= +1.20679158 \pm 1.4 \cdot 10^{-6} \) \(a_{54}= +0.28229495 \pm 1.5 \cdot 10^{-6} \)
\(a_{55}= -0.55586718 \pm 1.2 \cdot 10^{-6} \) \(a_{56}= +0.55298286 \pm 1.6 \cdot 10^{-6} \) \(a_{57}= -2.33236116 \pm 9.9 \cdot 10^{-7} \)
\(a_{58}= +0.99411245 \pm 2.0 \cdot 10^{-6} \) \(a_{59}= +0.90224468 \pm 1.0 \cdot 10^{-6} \) \(a_{60}= +0.33654514 \pm 1.3 \cdot 10^{-6} \)

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