Properties

Label 6.21
Level 66
Weight 00
Character 6.1
Symmetry even
RR 11.31308
Fricke sign +1+1

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Maass form invariants

Level: 6=23 6 = 2 \cdot 3
Weight: 0 0
Character: 6.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 11.3130895988813168021058701142±2101011.3130895988813168021058701142 \pm 2 \cdot 10^{-10}

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=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=0.14054347±1108a_{5}= -0.14054347 \pm 1 \cdot 10^{-8} a6=+0.40824829±1.0108a_{6}= +0.40824829 \pm 1.0 \cdot 10^{-8}
a7=+1.15074894±1108a_{7}= +1.15074894 \pm 1 \cdot 10^{-8} a8=+0.35355339±4.2108a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.09937924±1.0108a_{10}= -0.09937924 \pm 1.0 \cdot 10^{-8} a11=0.99003837±1108a_{11}= -0.99003837 \pm 1 \cdot 10^{-8} a12=+0.28867513±5.2108a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8}
a13=+1.12273858±1108a_{13}= +1.12273858 \pm 1 \cdot 10^{-8} a14=+0.81370238±1.0108a_{14}= +0.81370238 \pm 1.0 \cdot 10^{-8} a15=0.08114281±1.0108a_{15}= -0.08114281 \pm 1.0 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=+0.58801406±1108a_{17}= +0.58801406 \pm 1 \cdot 10^{-8} a18=+0.23570226±7.3108a_{18}= +0.23570226 \pm 7.3 \cdot 10^{-8}
a19=+1.90355331±1108a_{19}= +1.90355331 \pm 1 \cdot 10^{-8} a20=0.07027174±1.0108a_{20}= -0.07027174 \pm 1.0 \cdot 10^{-8} a21=+0.66438521±1.0108a_{21}= +0.66438521 \pm 1.0 \cdot 10^{-8}
a22=0.70006284±1.0108a_{22}= -0.70006284 \pm 1.0 \cdot 10^{-8} a23=+0.35455201±1108a_{23}= +0.35455201 \pm 1 \cdot 10^{-8} a24=+0.20412415±9.4108a_{24}= +0.20412415 \pm 9.4 \cdot 10^{-8}
a25=0.98024753±1108a_{25}= -0.98024753 \pm 1 \cdot 10^{-8} a26=+0.79389607±1.0108a_{26}= +0.79389607 \pm 1.0 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+0.57537447±1.0108a_{28}= +0.57537447 \pm 1.0 \cdot 10^{-8} a29=+0.81829811±1108a_{29}= +0.81829811 \pm 1 \cdot 10^{-8} a30=0.05737663±1.0108a_{30}= -0.05737663 \pm 1.0 \cdot 10^{-8}
a31=1.19963417±1108a_{31}= -1.19963417 \pm 1 \cdot 10^{-8} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=0.57159892±1.0108a_{33}= -0.57159892 \pm 1.0 \cdot 10^{-8}
a34=+0.41578873±1.0108a_{34}= +0.41578873 \pm 1.0 \cdot 10^{-8} a35=0.16173025±1108a_{35}= -0.16173025 \pm 1 \cdot 10^{-8} a36=+0.16666667±1.0107a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7}
a37=0.83256764±1108a_{37}= -0.83256764 \pm 1 \cdot 10^{-8} a38=+1.34601545±1.0108a_{38}= +1.34601545 \pm 1.0 \cdot 10^{-8} a39=+0.64821342±1.0108a_{39}= +0.64821342 \pm 1.0 \cdot 10^{-8}
a40=0.04968962±1.0108a_{40}= -0.04968962 \pm 1.0 \cdot 10^{-8} a41=1.52261685±1108a_{41}= -1.52261685 \pm 1 \cdot 10^{-8} a42=+0.46979129±1.0108a_{42}= +0.46979129 \pm 1.0 \cdot 10^{-8}
a43=+0.97696308±1108a_{43}= +0.97696308 \pm 1 \cdot 10^{-8} a44=0.49501918±1.0108a_{44}= -0.49501918 \pm 1.0 \cdot 10^{-8} a45=0.04684782±1.0108a_{45}= -0.04684782 \pm 1.0 \cdot 10^{-8}
a46=+0.25070613±1.0108a_{46}= +0.25070613 \pm 1.0 \cdot 10^{-8} a47=1.22991819±1108a_{47}= -1.22991819 \pm 1 \cdot 10^{-8} a48=+0.14433757±1.5107a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7}
a49=+0.32422313±1108a_{49}= +0.32422313 \pm 1 \cdot 10^{-8} a50=0.69313968±1.0108a_{50}= -0.69313968 \pm 1.0 \cdot 10^{-8} a51=+0.33949007±1.0108a_{51}= +0.33949007 \pm 1.0 \cdot 10^{-8}
a52=+0.56136929±1.0108a_{52}= +0.56136929 \pm 1.0 \cdot 10^{-8} a53=0.15975122±1108a_{53}= -0.15975122 \pm 1 \cdot 10^{-8} a54=+0.13608276±1.6107a_{54}= +0.13608276 \pm 1.6 \cdot 10^{-7}
a55=+0.13914343±1108a_{55}= +0.13914343 \pm 1 \cdot 10^{-8} a56=+0.40685119±1.0108a_{56}= +0.40685119 \pm 1.0 \cdot 10^{-8} a57=+1.09901701±1.0108a_{57}= +1.09901701 \pm 1.0 \cdot 10^{-8}
a58=+0.57862414±1.0108a_{58}= +0.57862414 \pm 1.0 \cdot 10^{-8} a59=1.47834962±1108a_{59}= -1.47834962 \pm 1 \cdot 10^{-8} a60=0.04057141±1.0108a_{60}= -0.04057141 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000