Properties

Label 14.11
Level 1414
Weight 00
Character 14.1
Symmetry odd
RR 4.589405
Fricke sign 1-1

Related objects

Downloads

Learn more

Maass form invariants

Level: 14=27 14 = 2 \cdot 7
Weight: 0 0
Character: 14.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 4.58940589266960591223447404034±1010124.58940589266960591223447404034 \pm 10 \cdot 10^{-12}

Maass form coefficients

The coefficients here are shown to at most 88 digits of precision. Full precision coefficients are available in the downloads.

a1=+1a_{1}= +1 a2=0.70710678±1.0108a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} a3=0.98353672±1108a_{3}= -0.98353672 \pm 1 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=+0.54739212±1108a_{5}= +0.54739212 \pm 1 \cdot 10^{-8} a6=+0.69546548±1.6108a_{6}= +0.69546548 \pm 1.6 \cdot 10^{-8}
a7=+0.37796447±1.0108a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} a8=0.35355339±4.2108a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} a9=0.03265553±1108a_{9}= -0.03265553 \pm 1 \cdot 10^{-8}
a10=0.38706468±1.5108a_{10}= -0.38706468 \pm 1.5 \cdot 10^{-8} a11=+1.49404316±1108a_{11}= +1.49404316 \pm 1 \cdot 10^{-8} a12=0.49176836±1.6108a_{12}= -0.49176836 \pm 1.6 \cdot 10^{-8}
a13=+1.24705038±1108a_{13}= +1.24705038 \pm 1 \cdot 10^{-8} a14=0.26726124±1.0108a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} a15=0.53838024±1108a_{15}= -0.53838024 \pm 1 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=0.55348948±1108a_{17}= -0.55348948 \pm 1 \cdot 10^{-8} a18=+0.02309094±1.5108a_{18}= +0.02309094 \pm 1.5 \cdot 10^{-8}
a19=+0.38706721±1108a_{19}= +0.38706721 \pm 1 \cdot 10^{-8} a20=+0.27369606±1.5108a_{20}= +0.27369606 \pm 1.5 \cdot 10^{-8} a21=0.37174194±1.6108a_{21}= -0.37174194 \pm 1.6 \cdot 10^{-8}
a22=1.05644805±1.5108a_{22}= -1.05644805 \pm 1.5 \cdot 10^{-8} a23=+0.73198177±1108a_{23}= +0.73198177 \pm 1 \cdot 10^{-8} a24=+0.34773274±1.6108a_{24}= +0.34773274 \pm 1.6 \cdot 10^{-8}
a25=0.70036187±1108a_{25}= -0.70036187 \pm 1 \cdot 10^{-8} a26=0.88179778±1.5108a_{26}= -0.88179778 \pm 1.5 \cdot 10^{-8} a27=+1.01565463±1108a_{27}= +1.01565463 \pm 1 \cdot 10^{-8}
a28=+0.18898224±9.4108a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} a29=+1.56246294±1108a_{29}= +1.56246294 \pm 1 \cdot 10^{-8} a30=+0.38069232±2.1108a_{30}= +0.38069232 \pm 2.1 \cdot 10^{-8}
a31=+0.22664571±1108a_{31}= +0.22664571 \pm 1 \cdot 10^{-8} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=1.46944630±1108a_{33}= -1.46944630 \pm 1 \cdot 10^{-8}
a34=+0.39137616±1.3108a_{34}= +0.39137616 \pm 1.3 \cdot 10^{-8} a35=+0.20689477±1.5108a_{35}= +0.20689477 \pm 1.5 \cdot 10^{-8} a36=0.01632776±1.5108a_{36}= -0.01632776 \pm 1.5 \cdot 10^{-8}
a37=1.64103625±1108a_{37}= -1.64103625 \pm 1 \cdot 10^{-8} a38=0.27369785±1.5108a_{38}= -0.27369785 \pm 1.5 \cdot 10^{-8} a39=1.22651984±1108a_{39}= -1.22651984 \pm 1 \cdot 10^{-8}
a40=0.19353234±1.5108a_{40}= -0.19353234 \pm 1.5 \cdot 10^{-8} a41=+1.50447766±1108a_{41}= +1.50447766 \pm 1 \cdot 10^{-8} a42=+0.26286124±1.6108a_{42}= +0.26286124 \pm 1.6 \cdot 10^{-8}
a43=+0.29583513±1108a_{43}= +0.29583513 \pm 1 \cdot 10^{-8} a44=+0.74702158±1.5108a_{44}= +0.74702158 \pm 1.5 \cdot 10^{-8} a45=0.01787538±1108a_{45}= -0.01787538 \pm 1 \cdot 10^{-8}
a46=0.51758927±1.4108a_{46}= -0.51758927 \pm 1.4 \cdot 10^{-8} a47=+1.01760252±1108a_{47}= +1.01760252 \pm 1 \cdot 10^{-8} a48=0.24588418±1.6108a_{48}= -0.24588418 \pm 1.6 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=+0.49523063±1.4108a_{50}= +0.49523063 \pm 1.4 \cdot 10^{-8} a51=+0.54437722±1108a_{51}= +0.54437722 \pm 1 \cdot 10^{-8}
a52=+0.62352519±1.5108a_{52}= +0.62352519 \pm 1.5 \cdot 10^{-8} a53=1.66998253±1108a_{53}= -1.66998253 \pm 1 \cdot 10^{-8} a54=0.71817627±1.5108a_{54}= -0.71817627 \pm 1.5 \cdot 10^{-8}
a55=+0.81782745±1108a_{55}= +0.81782745 \pm 1 \cdot 10^{-8} a56=0.13363062±1.6107a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} a57=0.38069481±1108a_{57}= -0.38069481 \pm 1 \cdot 10^{-8}
a58=1.10482814±1.5108a_{58}= -1.10482814 \pm 1.5 \cdot 10^{-8} a59=+1.16513110±1108a_{59}= +1.16513110 \pm 1 \cdot 10^{-8} a60=0.26919012±2.1108a_{60}= -0.26919012 \pm 2.1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000