Properties

Label 14.25
Level $14$
Weight $0$
Character 14.1
Symmetry even
\(R\) 6.964851
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(6.96485168305122464530462526309 \pm 3 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -1.88936626 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.78161232 \pm 1 \cdot 10^{-8} \) \(a_{6}= +1.33598369 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +2.56970486 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.55268337 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -1.27677997 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.94468313 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= +0.78230652 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -1.47675194 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.06992502 \pm 1 \cdot 10^{-8} \) \(a_{18}= -1.81705574 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= +0.23228949 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.39080616 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -0.71411332 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.90281978 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +0.55490287 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.66799185 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= -0.38908219 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.55317424 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= -2.96574741 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} \) \(a_{29}= +0.36135131 \pm 1 \cdot 10^{-8} \) \(a_{30}= +1.04422131 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -1.60476229 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +2.41230500 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.04944445 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= +0.29542169 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= +1.28485243 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= +0.20362386 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.16425348 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= -1.47806354 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.27634168 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -1.88617222 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.50495437 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.59588814 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.63838999 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= +2.00851297 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.39237558 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= -1.20465953 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.47234156 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.27512265 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.13211397 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.39115326 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= +0.02174945 \pm 1 \cdot 10^{-8} \) \(a_{54}= +2.09710010 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= -0.99794695 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} \) \(a_{57}= -0.43887993 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.25551396 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= +0.58209352 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.73837597 \pm 1.0 \cdot 10^{-8} \)

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