Properties

Label 14.61
Level $14$
Weight $0$
Character 14.1
Symmetry odd
\(R\) 11.11343
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(11.1134306546693979915166355651 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.66654851 \pm 1.2 \cdot 10^{-5} \)
\(a_{4}= +0.5 \) \(a_{5}= +1.34901476 \pm 9.8 \cdot 10^{-6} \) \(a_{6}= -1.17842775 \pm 1.2 \cdot 10^{-5} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +1.77738393 \pm 9.9 \cdot 10^{-6} \)
\(a_{10}= -0.95389749 \pm 9.8 \cdot 10^{-6} \) \(a_{11}= +1.67397663 \pm 1.0 \cdot 10^{-5} \) \(a_{12}= +0.83327425 \pm 1.2 \cdot 10^{-5} \)
\(a_{13}= +0.78093275 \pm 9.4 \cdot 10^{-6} \) \(a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +2.24819854 \pm 1.2 \cdot 10^{-5} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.00113081 \pm 6.5 \cdot 10^{-6} \) \(a_{18}= -1.25680023 \pm 9.9 \cdot 10^{-6} \)
\(a_{19}= -1.07438278 \pm 9.7 \cdot 10^{-6} \) \(a_{20}= +0.67450738 \pm 9.8 \cdot 10^{-6} \) \(a_{21}= +0.62989613 \pm 1.2 \cdot 10^{-5} \)
\(a_{22}= -1.18368023 \pm 1.0 \cdot 10^{-5} \) \(a_{23}= -1.05654566 \pm 8.9 \cdot 10^{-6} \) \(a_{24}= -0.58921388 \pm 1.2 \cdot 10^{-5} \)
\(a_{25}= +0.81984083 \pm 7.6 \cdot 10^{-6} \) \(a_{26}= -0.55220284 \pm 9.4 \cdot 10^{-6} \) \(a_{27}= +1.29554802 \pm 9.3 \cdot 10^{-6} \)
\(a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= -1.30218890 \pm 1.0 \cdot 10^{-5} \) \(a_{30}= -1.58971643 \pm 2.2 \cdot 10^{-5} \)
\(a_{31}= +0.62470357 \pm 1.0 \cdot 10^{-5} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +2.78976326 \pm 1.1 \cdot 10^{-5} \)
\(a_{34}= -0.00079960 \pm 6.5 \cdot 10^{-6} \) \(a_{35}= +0.50987965 \pm 9.8 \cdot 10^{-6} \) \(a_{36}= +0.88869196 \pm 9.9 \cdot 10^{-6} \)
\(a_{37}= +0.48026224 \pm 7.7 \cdot 10^{-6} \) \(a_{38}= +0.75970335 \pm 9.7 \cdot 10^{-6} \) \(a_{39}= +1.30146231 \pm 1.0 \cdot 10^{-5} \)
\(a_{40}= -0.47694874 \pm 9.8 \cdot 10^{-6} \) \(a_{41}= -1.27324812 \pm 6.3 \cdot 10^{-6} \) \(a_{42}= -0.44540382 \pm 1.2 \cdot 10^{-5} \)
\(a_{43}= -1.25735185 \pm 9.9 \cdot 10^{-6} \) \(a_{44}= +0.83698832 \pm 1.0 \cdot 10^{-5} \) \(a_{45}= +2.39771716 \pm 8.7 \cdot 10^{-6} \)
\(a_{46}= +0.74709060 \pm 8.9 \cdot 10^{-6} \) \(a_{47}= +0.12459623 \pm 7.1 \cdot 10^{-6} \) \(a_{48}= +0.41663713 \pm 1.2 \cdot 10^{-5} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.57971501 \pm 7.6 \cdot 10^{-6} \) \(a_{51}= +0.00188455 \pm 7.6 \cdot 10^{-6} \)
\(a_{52}= +0.39046637 \pm 9.4 \cdot 10^{-6} \) \(a_{53}= -0.52923718 \pm 9.5 \cdot 10^{-6} \) \(a_{54}= -0.91609079 \pm 9.3 \cdot 10^{-6} \)
\(a_{55}= +2.25821919 \pm 9.3 \cdot 10^{-6} \) \(a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= -1.79051102 \pm 1.3 \cdot 10^{-5} \)
\(a_{58}= +0.92078660 \pm 1.0 \cdot 10^{-5} \) \(a_{59}= +1.35801779 \pm 1.0 \cdot 10^{-5} \) \(a_{60}= +1.12409927 \pm 2.2 \cdot 10^{-5} \)

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