Properties

Label 14.84
Level 1414
Weight 00
Character 14.1
Symmetry even
RR 12.97071
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: even
Fricke sign: +1+1
Spectral parameter: 12.9707194030509437521312479484±310812.9707194030509437521312479484 \pm 3 \cdot 10^{-8}

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=+0.82138308±1.7107a_{3}= +0.82138308 \pm 1.7 \cdot 10^{-7}
a4=+0.5a_{4}= +0.5 a5=1.80718382±2.6107a_{5}= -1.80718382 \pm 2.6 \cdot 10^{-7} a6=+0.58080554±1.8107a_{6}= +0.58080554 \pm 1.8 \cdot 10^{-7}
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=0.32532984±2.4107a_{9}= -0.32532984 \pm 2.4 \cdot 10^{-7}
a10=1.27787194±2.7107a_{10}= -1.27787194 \pm 2.7 \cdot 10^{-7} a11=0.76289104±3.1107a_{11}= -0.76289104 \pm 3.1 \cdot 10^{-7} a12=+0.41069154±1.8107a_{12}= +0.41069154 \pm 1.8 \cdot 10^{-7}
a13=+0.78738989±2.2107a_{13}= +0.78738989 \pm 2.2 \cdot 10^{-7} a14=+0.26726124±1.0108a_{14}= +0.26726124 \pm 1.0 \cdot 10^{-8} a15=1.48439021±1.8107a_{15}= -1.48439021 \pm 1.8 \cdot 10^{-7}
a16=+0.25a_{16}= +0.25 a17=+1.00193573±2.9107a_{17}= +1.00193573 \pm 2.9 \cdot 10^{-7} a18=0.23004294±2.5107a_{18}= -0.23004294 \pm 2.5 \cdot 10^{-7}
a19=+1.05939729±1.9107a_{19}= +1.05939729 \pm 1.9 \cdot 10^{-7} a20=0.90359191±2.7107a_{20}= -0.90359191 \pm 2.7 \cdot 10^{-7} a21=+0.31045362±1.8107a_{21}= +0.31045362 \pm 1.8 \cdot 10^{-7}
a22=0.53944543±3.2107a_{22}= -0.53944543 \pm 3.2 \cdot 10^{-7} a23=+1.69178660±1.5107a_{23}= +1.69178660 \pm 1.5 \cdot 10^{-7} a24=+0.29040277±1.8107a_{24}= +0.29040277 \pm 1.8 \cdot 10^{-7}
a25=+2.26591337±3.1107a_{25}= +2.26591337 \pm 3.1 \cdot 10^{-7} a26=+0.55676873±2.3107a_{26}= +0.55676873 \pm 2.3 \cdot 10^{-7} a27=1.08860350±1.9107a_{27}= -1.08860350 \pm 1.9 \cdot 10^{-7}
a28=+0.18898224±9.4108a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} a29=+0.95218856±2.4107a_{29}= +0.95218856 \pm 2.4 \cdot 10^{-7} a30=1.04962238±4.5107a_{30}= -1.04962238 \pm 4.5 \cdot 10^{-7}
a31=0.78276390±2.8107a_{31}= -0.78276390 \pm 2.8 \cdot 10^{-7} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=0.62662579±1.6107a_{33}= -0.62662579 \pm 1.6 \cdot 10^{-7}
a34=+0.70847555±3.0107a_{34}= +0.70847555 \pm 3.0 \cdot 10^{-7} a35=0.68305128±2.7107a_{35}= -0.68305128 \pm 2.7 \cdot 10^{-7} a36=0.16266492±2.5107a_{36}= -0.16266492 \pm 2.5 \cdot 10^{-7}
a37=+0.36741876±1.2107a_{37}= +0.36741876 \pm 1.2 \cdot 10^{-7} a38=+0.74910701±2.0107a_{38}= +0.74910701 \pm 2.0 \cdot 10^{-7} a39=+0.64674873±2.5107a_{39}= +0.64674873 \pm 2.5 \cdot 10^{-7}
a40=0.63893597±2.7107a_{40}= -0.63893597 \pm 2.7 \cdot 10^{-7} a41=+0.82264413±2.5107a_{41}= +0.82264413 \pm 2.5 \cdot 10^{-7} a42=+0.21952386±1.8107a_{42}= +0.21952386 \pm 1.8 \cdot 10^{-7}
a43=0.97907934±1.7107a_{43}= -0.97907934 \pm 1.7 \cdot 10^{-7} a44=0.38144552±3.2107a_{44}= -0.38144552 \pm 3.2 \cdot 10^{-7} a45=+0.58793083±2.6107a_{45}= +0.58793083 \pm 2.6 \cdot 10^{-7}
a46=+1.19627377±1.6107a_{46}= +1.19627377 \pm 1.6 \cdot 10^{-7} a47=0.47825688±2.1107a_{47}= -0.47825688 \pm 2.1 \cdot 10^{-7} a48=+0.20534577±1.8107a_{48}= +0.20534577 \pm 1.8 \cdot 10^{-7}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=+1.60224271±3.2107a_{50}= +1.60224271 \pm 3.2 \cdot 10^{-7} a51=+0.82297305±1.4107a_{51}= +0.82297305 \pm 1.4 \cdot 10^{-7}
a52=+0.39369495±2.3107a_{52}= +0.39369495 \pm 2.3 \cdot 10^{-7} a53=+0.27318282±2.8107a_{53}= +0.27318282 \pm 2.8 \cdot 10^{-7} a54=0.76975892±2.0107a_{54}= -0.76975892 \pm 2.0 \cdot 10^{-7}
a55=+1.37868435±2.8107a_{55}= +1.37868435 \pm 2.8 \cdot 10^{-7} a56=+0.13363062±1.6107a_{56}= +0.13363062 \pm 1.6 \cdot 10^{-7} a57=+0.87017101±1.6107a_{57}= +0.87017101 \pm 1.6 \cdot 10^{-7}
a58=+0.67329899±2.5107a_{58}= +0.67329899 \pm 2.5 \cdot 10^{-7} a59=+0.00319503±2.2107a_{59}= +0.00319503 \pm 2.2 \cdot 10^{-7} a60=0.74219510±4.5107a_{60}= -0.74219510 \pm 4.5 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000