Properties

Label 6.42
Level 66
Weight 00
Character 6.1
Symmetry odd
RR 16.04269
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: odd
Fricke sign: +1+1
Spectral parameter: 16.0426930590212746595448890985±310716.0426930590212746595448890985 \pm 3 \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=0.57735027±1.0108a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=+1.36060894±3.4104a_{5}= +1.36060894 \pm 3.4 \cdot 10^{-4} a6=+0.40824829±1.0108a_{6}= +0.40824829 \pm 1.0 \cdot 10^{-8}
a7=1.80473738±3.4104a_{7}= -1.80473738 \pm 3.4 \cdot 10^{-4} 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=0.96209580±3.4104a_{10}= -0.96209580 \pm 3.4 \cdot 10^{-4} a11=+0.17474705±2.7104a_{11}= +0.17474705 \pm 2.7 \cdot 10^{-4} a12=0.28867513±5.2108a_{12}= -0.28867513 \pm 5.2 \cdot 10^{-8}
a13=+0.44448836±4.5104a_{13}= +0.44448836 \pm 4.5 \cdot 10^{-4} a14=+1.27614204±3.4104a_{14}= +1.27614204 \pm 3.4 \cdot 10^{-4} a15=0.78554793±3.4104a_{15}= -0.78554793 \pm 3.4 \cdot 10^{-4}
a16=+0.25a_{16}= +0.25 a17=+1.44230049±2.7104a_{17}= +1.44230049 \pm 2.7 \cdot 10^{-4} a18=0.23570226±7.3108a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8}
a19=1.21873231±6.1104a_{19}= -1.21873231 \pm 6.1 \cdot 10^{-4} a20=+0.68030447±3.4104a_{20}= +0.68030447 \pm 3.4 \cdot 10^{-4} a21=+1.04196561±3.4104a_{21}= +1.04196561 \pm 3.4 \cdot 10^{-4}
a22=0.12356483±2.7104a_{22}= -0.12356483 \pm 2.7 \cdot 10^{-4} a23=+1.28038308±4.3104a_{23}= +1.28038308 \pm 4.3 \cdot 10^{-4} a24=+0.20412415±9.4108a_{24}= +0.20412415 \pm 9.4 \cdot 10^{-8}
a25=+0.85125667±3.3104a_{25}= +0.85125667 \pm 3.3 \cdot 10^{-4} a26=0.31430073±4.5104a_{26}= -0.31430073 \pm 4.5 \cdot 10^{-4} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.90236869±3.4104a_{28}= -0.90236869 \pm 3.4 \cdot 10^{-4} a29=0.53200567±3.2104a_{29}= -0.53200567 \pm 3.2 \cdot 10^{-4} a30=+0.55546627±3.4104a_{30}= +0.55546627 \pm 3.4 \cdot 10^{-4}
a31=0.18049367±5.6104a_{31}= -0.18049367 \pm 5.6 \cdot 10^{-4} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=0.10089026±2.7104a_{33}= -0.10089026 \pm 2.7 \cdot 10^{-4}
a34=1.01986045±2.7104a_{34}= -1.01986045 \pm 2.7 \cdot 10^{-4} a35=2.45554180±2.7104a_{35}= -2.45554180 \pm 2.7 \cdot 10^{-4} a36=+0.16666667±1.0107a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7}
a37=0.96606237±4.8104a_{37}= -0.96606237 \pm 4.8 \cdot 10^{-4} a38=+0.86177388±6.1104a_{38}= +0.86177388 \pm 6.1 \cdot 10^{-4} a39=0.25662547±4.5104a_{39}= -0.25662547 \pm 4.5 \cdot 10^{-4}
a40=0.48104790±3.4104a_{40}= -0.48104790 \pm 3.4 \cdot 10^{-4} a41=+0.14736262±2.6104a_{41}= +0.14736262 \pm 2.6 \cdot 10^{-4} a42=0.73678095±3.4104a_{42}= -0.73678095 \pm 3.4 \cdot 10^{-4}
a43=0.22838398±2.6104a_{43}= -0.22838398 \pm 2.6 \cdot 10^{-4} a44=+0.08737353±2.7104a_{44}= +0.08737353 \pm 2.7 \cdot 10^{-4} a45=+0.45353631±3.4104a_{45}= +0.45353631 \pm 3.4 \cdot 10^{-4}
a46=0.90536756±4.3104a_{46}= -0.90536756 \pm 4.3 \cdot 10^{-4} a47=1.53413251±3.9104a_{47}= -1.53413251 \pm 3.9 \cdot 10^{-4} a48=0.14433757±1.5107a_{48}= -0.14433757 \pm 1.5 \cdot 10^{-7}
a49=+2.25707700±3.8104a_{49}= +2.25707700 \pm 3.8 \cdot 10^{-4} a50=0.60192937±3.3104a_{50}= -0.60192937 \pm 3.3 \cdot 10^{-4} a51=0.83271257±2.7104a_{51}= -0.83271257 \pm 2.7 \cdot 10^{-4}
a52=+0.22224418±4.5104a_{52}= +0.22224418 \pm 4.5 \cdot 10^{-4} a53=0.55238004±6.0104a_{53}= -0.55238004 \pm 6.0 \cdot 10^{-4} a54=+0.13608276±1.6107a_{54}= +0.13608276 \pm 1.6 \cdot 10^{-7}
a55=+0.23776240±2.9104a_{55}= +0.23776240 \pm 2.9 \cdot 10^{-4} a56=+0.63807102±3.4104a_{56}= +0.63807102 \pm 3.4 \cdot 10^{-4} a57=+0.70363543±6.1104a_{57}= +0.70363543 \pm 6.1 \cdot 10^{-4}
a58=+0.37618481±3.2104a_{58}= +0.37618481 \pm 3.2 \cdot 10^{-4} a59=1.42346803±4.8104a_{59}= -1.42346803 \pm 4.8 \cdot 10^{-4} a60=0.39277397±3.4104a_{60}= -0.39277397 \pm 3.4 \cdot 10^{-4}

Displaying ana_n with nn up to: 60 180 1000