Properties

Label 14.7
Level 1414
Weight 00
Character 14.1
Symmetry odd
RR 3.716548
Fricke sign 1-1

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Maass form invariants

Level: 14=27 14 = 2 \cdot 7
Weight: 0 0
Character: 14.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 3.71654847808296773906123655693±510123.71654847808296773906123655693 \pm 5 \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=+1.75081033±1108a_{3}= +1.75081033 \pm 1 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=+0.59303407±1108a_{5}= +0.59303407 \pm 1 \cdot 10^{-8} a6=1.23800986±1.4108a_{6}= -1.23800986 \pm 1.4 \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=+2.06533683±1108a_{9}= +2.06533683 \pm 1 \cdot 10^{-8}
a10=0.41933841±1.3108a_{10}= -0.41933841 \pm 1.3 \cdot 10^{-8} a11=0.67434613±1108a_{11}= -0.67434613 \pm 1 \cdot 10^{-8} a12=+0.87540517±1.4108a_{12}= +0.87540517 \pm 1.4 \cdot 10^{-8}
a13=0.89956731±1108a_{13}= -0.89956731 \pm 1 \cdot 10^{-8} a14=0.26726124±1.0108a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} a15=+1.03829018±1108a_{15}= +1.03829018 \pm 1 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=+0.66977162±1108a_{17}= +0.66977162 \pm 1 \cdot 10^{-8} a18=1.46041367±1.3108a_{18}= -1.46041367 \pm 1.3 \cdot 10^{-8}
a19=1.73829756±1108a_{19}= -1.73829756 \pm 1 \cdot 10^{-8} a20=+0.29651704±1.3108a_{20}= +0.29651704 \pm 1.3 \cdot 10^{-8} a21=+0.66174411±1.4108a_{21}= +0.66174411 \pm 1.4 \cdot 10^{-8}
a22=+0.47683472±1.3108a_{22}= +0.47683472 \pm 1.3 \cdot 10^{-8} a23=+0.83161743±1108a_{23}= +0.83161743 \pm 1 \cdot 10^{-8} a24=0.61900493±1.4108a_{24}= -0.61900493 \pm 1.4 \cdot 10^{-8}
a25=0.64831059±1108a_{25}= -0.64831059 \pm 1 \cdot 10^{-8} a26=+0.63609014±1.3108a_{26}= +0.63609014 \pm 1.3 \cdot 10^{-8} a27=+1.86520272±1108a_{27}= +1.86520272 \pm 1 \cdot 10^{-8}
a28=+0.18898224±9.4108a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} a29=0.34267426±1108a_{29}= -0.34267426 \pm 1 \cdot 10^{-8} a30=0.73418203±1.7108a_{30}= -0.73418203 \pm 1.7 \cdot 10^{-8}
a31=0.36151347±1108a_{31}= -0.36151347 \pm 1 \cdot 10^{-8} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=1.18065218±1108a_{33}= -1.18065218 \pm 1 \cdot 10^{-8}
a34=0.47360005±1.2108a_{34}= -0.47360005 \pm 1.2 \cdot 10^{-8} a35=+0.22414581±1.3108a_{35}= +0.22414581 \pm 1.3 \cdot 10^{-8} a36=+1.03266841±1.3108a_{36}= +1.03266841 \pm 1.3 \cdot 10^{-8}
a37=0.22887846±1108a_{37}= -0.22887846 \pm 1 \cdot 10^{-8} a38=+1.22916199±1.3108a_{38}= +1.22916199 \pm 1.3 \cdot 10^{-8} a39=1.57497174±1108a_{39}= -1.57497174 \pm 1 \cdot 10^{-8}
a40=0.20966921±1.3108a_{40}= -0.20966921 \pm 1.3 \cdot 10^{-8} a41=0.04153373±1108a_{41}= -0.04153373 \pm 1 \cdot 10^{-8} a42=0.46792374±1.4108a_{42}= -0.46792374 \pm 1.4 \cdot 10^{-8}
a43=+0.62800368±1108a_{43}= +0.62800368 \pm 1 \cdot 10^{-8} a44=0.33717307±1.3108a_{44}= -0.33717307 \pm 1.3 \cdot 10^{-8} a45=+1.22481511±1108a_{45}= +1.22481511 \pm 1 \cdot 10^{-8}
a46=0.58804233±1.3108a_{46}= -0.58804233 \pm 1.3 \cdot 10^{-8} a47=+1.17366232±1108a_{47}= +1.17366232 \pm 1 \cdot 10^{-8} a48=+0.43770258±1.4108a_{48}= +0.43770258 \pm 1.4 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=+0.45842481±1.2108a_{50}= +0.45842481 \pm 1.2 \cdot 10^{-8} a51=+1.17264307±1108a_{51}= +1.17264307 \pm 1 \cdot 10^{-8}
a52=0.44978365±1.3108a_{52}= -0.44978365 \pm 1.3 \cdot 10^{-8} a53=0.14101023±1108a_{53}= -0.14101023 \pm 1 \cdot 10^{-8} a54=1.31889749±1.3108a_{54}= -1.31889749 \pm 1.3 \cdot 10^{-8}
a55=0.39991023±1108a_{55}= -0.39991023 \pm 1 \cdot 10^{-8} a56=0.13363062±1.6107a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} a57=3.04342933±1108a_{57}= -3.04342933 \pm 1 \cdot 10^{-8}
a58=+0.24230730±1.3108a_{58}= +0.24230730 \pm 1.3 \cdot 10^{-8} a59=0.03739206±1108a_{59}= -0.03739206 \pm 1 \cdot 10^{-8} a60=+0.51914509±1.7108a_{60}= +0.51914509 \pm 1.7 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000