Properties

Label 2.14
Level 22
Weight 00
Character 2.1
Symmetry even
RR 15.31419
Fricke sign 1-1

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Maass form invariants

Level: 2 2
Weight: 0 0
Character: 2.1
Symmetry: even
Fricke sign: 1-1
Spectral parameter: 15.3141965841790996306418247371±210715.3141965841790996306418247371 \pm 2 \cdot 10^{-7}

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=0.05270933±1108a_{3}= -0.05270933 \pm 1 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=1.41821650±1108a_{5}= -1.41821650 \pm 1 \cdot 10^{-8} a6=0.03727112±1.3108a_{6}= -0.03727112 \pm 1.3 \cdot 10^{-8}
a7=+0.26666023±1108a_{7}= +0.26666023 \pm 1 \cdot 10^{-8} a8=+0.35355339±4.2108a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} a9=0.99722173±1108a_{9}= -0.99722173 \pm 1 \cdot 10^{-8}
a10=1.00283050±1.3108a_{10}= -1.00283050 \pm 1.3 \cdot 10^{-8} a11=0.86652814±1108a_{11}= -0.86652814 \pm 1 \cdot 10^{-8} a12=0.02635466±1.3108a_{12}= -0.02635466 \pm 1.3 \cdot 10^{-8}
a13=1.35196476±1108a_{13}= -1.35196476 \pm 1 \cdot 10^{-8} a14=+0.18855726±1.3108a_{14}= +0.18855726 \pm 1.3 \cdot 10^{-8} a15=+0.07475324±1108a_{15}= +0.07475324 \pm 1 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=0.74279692±1108a_{17}= -0.74279692 \pm 1 \cdot 10^{-8} a18=0.70514225±1.1108a_{18}= -0.70514225 \pm 1.1 \cdot 10^{-8}
a19=+1.76178013±1108a_{19}= +1.76178013 \pm 1 \cdot 10^{-8} a20=0.70910825±1.3108a_{20}= -0.70910825 \pm 1.3 \cdot 10^{-8} a21=0.01405548±1108a_{21}= -0.01405548 \pm 1 \cdot 10^{-8}
a22=0.61272793±1.2108a_{22}= -0.61272793 \pm 1.2 \cdot 10^{-8} a23=+0.30024567±1108a_{23}= +0.30024567 \pm 1 \cdot 10^{-8} a24=0.01863556±1.3108a_{24}= -0.01863556 \pm 1.3 \cdot 10^{-8}
a25=+1.01133804±1108a_{25}= +1.01133804 \pm 1 \cdot 10^{-8} a26=0.95598345±1.3108a_{26}= -0.95598345 \pm 1.3 \cdot 10^{-8} a27=+0.10527222±1108a_{27}= +0.10527222 \pm 1 \cdot 10^{-8}
a28=+0.13333012±1.3108a_{28}= +0.13333012 \pm 1.3 \cdot 10^{-8} a29=0.57033584±1108a_{29}= -0.57033584 \pm 1 \cdot 10^{-8} a30=+0.05285852±1.6108a_{30}= +0.05285852 \pm 1.6 \cdot 10^{-8}
a31=+0.71005260±1108a_{31}= +0.71005260 \pm 1 \cdot 10^{-8} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=+0.04567412±1108a_{33}= +0.04567412 \pm 1 \cdot 10^{-8}
a34=0.52523674±1.1108a_{34}= -0.52523674 \pm 1.1 \cdot 10^{-8} a35=0.37818194±1108a_{35}= -0.37818194 \pm 1 \cdot 10^{-8} a36=0.49861086±1.1108a_{36}= -0.49861086 \pm 1.1 \cdot 10^{-8}
a37=+0.38842085±1108a_{37}= +0.38842085 \pm 1 \cdot 10^{-8} a38=+1.24576667±1.2108a_{38}= +1.24576667 \pm 1.2 \cdot 10^{-8} a39=+0.07126115±1108a_{39}= +0.07126115 \pm 1 \cdot 10^{-8}
a40=0.50141525±1.3108a_{40}= -0.50141525 \pm 1.3 \cdot 10^{-8} a41=0.42764681±1108a_{41}= -0.42764681 \pm 1 \cdot 10^{-8} a42=0.00993873±1.6108a_{42}= -0.00993873 \pm 1.6 \cdot 10^{-8}
a43=0.49029491±1108a_{43}= -0.49029491 \pm 1 \cdot 10^{-8} a44=0.43326407±1.2108a_{44}= -0.43326407 \pm 1.2 \cdot 10^{-8} a45=+1.41427631±1108a_{45}= +1.41427631 \pm 1 \cdot 10^{-8}
a46=+0.21230575±1.0108a_{46}= +0.21230575 \pm 1.0 \cdot 10^{-8} a47=0.13804474±1108a_{47}= -0.13804474 \pm 1 \cdot 10^{-8} a48=0.01317733±1.3108a_{48}= -0.01317733 \pm 1.3 \cdot 10^{-8}
a49=0.92889232±1108a_{49}= -0.92889232 \pm 1 \cdot 10^{-8} a50=+0.71512398±1.1108a_{50}= +0.71512398 \pm 1.1 \cdot 10^{-8} a51=+0.03915233±1108a_{51}= +0.03915233 \pm 1 \cdot 10^{-8}
a52=0.67598238±1.3108a_{52}= -0.67598238 \pm 1.3 \cdot 10^{-8} a53=0.38061124±1108a_{53}= -0.38061124 \pm 1 \cdot 10^{-8} a54=+0.07443870±1.3108a_{54}= +0.07443870 \pm 1.3 \cdot 10^{-8}
a55=+1.22892451±1108a_{55}= +1.22892451 \pm 1 \cdot 10^{-8} a56=+0.09427863±1.3108a_{56}= +0.09427863 \pm 1.3 \cdot 10^{-8} a57=0.09286225±1108a_{57}= -0.09286225 \pm 1 \cdot 10^{-8}
a58=0.40328834±1.5108a_{58}= -0.40328834 \pm 1.5 \cdot 10^{-8} a59=+0.49612585±1108a_{59}= +0.49612585 \pm 1 \cdot 10^{-8} a60=+0.03737662±1.6108a_{60}= +0.03737662 \pm 1.6 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000