Properties

Label 6.18
Level 66
Weight 00
Character 6.1
Symmetry odd
RR 10.19612
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: 10.1961201777286022110710364105±3101110.1961201777286022110710364105 \pm 3 \cdot 10^{-11}

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=+1.16609433±3.4107a_{5}= +1.16609433 \pm 3.4 \cdot 10^{-7} a6=0.40824829±1.0108a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8}
a7=1.22121809±3.3107a_{7}= -1.22121809 \pm 3.3 \cdot 10^{-7} 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=0.82455321±3.5107a_{10}= -0.82455321 \pm 3.5 \cdot 10^{-7} a11=+0.66633898±2.6107a_{11}= +0.66633898 \pm 2.6 \cdot 10^{-7} a12=+0.28867513±5.2108a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8}
a13=+1.10843532±4.4107a_{13}= +1.10843532 \pm 4.4 \cdot 10^{-7} a14=+0.86353159±3.4107a_{14}= +0.86353159 \pm 3.4 \cdot 10^{-7} a15=+0.67324488±3.5107a_{15}= +0.67324488 \pm 3.5 \cdot 10^{-7}
a16=+0.25a_{16}= +0.25 a17=0.81084087±2.7107a_{17}= -0.81084087 \pm 2.7 \cdot 10^{-7} a18=0.23570226±7.3108a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8}
a19=+1.81939405±5.9107a_{19}= +1.81939405 \pm 5.9 \cdot 10^{-7} a20=+0.58304717±3.5107a_{20}= +0.58304717 \pm 3.5 \cdot 10^{-7} a21=0.70507059±3.4107a_{21}= -0.70507059 \pm 3.4 \cdot 10^{-7}
a22=0.47117281±2.7107a_{22}= -0.47117281 \pm 2.7 \cdot 10^{-7} a23=+0.90816965±4.2107a_{23}= +0.90816965 \pm 4.2 \cdot 10^{-7} a24=0.20412415±9.4108a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8}
a25=+0.35977600±3.2107a_{25}= +0.35977600 \pm 3.2 \cdot 10^{-7} a26=0.78378213±4.5107a_{26}= -0.78378213 \pm 4.5 \cdot 10^{-7} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.61060905±3.4107a_{28}= -0.61060905 \pm 3.4 \cdot 10^{-7} a29=+0.55744999±3.2107a_{29}= +0.55744999 \pm 3.2 \cdot 10^{-7} a30=0.47605602±3.5107a_{30}= -0.47605602 \pm 3.5 \cdot 10^{-7}
a31=+1.22404245±5.5107a_{31}= +1.22404245 \pm 5.5 \cdot 10^{-7} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=+0.38471099±2.7107a_{33}= +0.38471099 \pm 2.7 \cdot 10^{-7}
a34=+0.57335108±2.8107a_{34}= +0.57335108 \pm 2.8 \cdot 10^{-7} a35=1.42405550±2.6107a_{35}= -1.42405550 \pm 2.6 \cdot 10^{-7} a36=+0.16666667±1.0107a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7}
a37=+0.05711803±4.7107a_{37}= +0.05711803 \pm 4.7 \cdot 10^{-7} a38=1.28650587±6.0107a_{38}= -1.28650587 \pm 6.0 \cdot 10^{-7} a39=+0.63995543±4.5107a_{39}= +0.63995543 \pm 4.5 \cdot 10^{-7}
a40=0.41227661±3.5107a_{40}= -0.41227661 \pm 3.5 \cdot 10^{-7} a41=0.00975442±2.5107a_{41}= -0.00975442 \pm 2.5 \cdot 10^{-7} a42=+0.49856020±3.4107a_{42}= +0.49856020 \pm 3.4 \cdot 10^{-7}
a43=+1.35478126±2.5107a_{43}= +1.35478126 \pm 2.5 \cdot 10^{-7} a44=+0.33316949±2.7107a_{44}= +0.33316949 \pm 2.7 \cdot 10^{-7} a45=+0.38869811±3.5107a_{45}= +0.38869811 \pm 3.5 \cdot 10^{-7}
a46=0.64217292±4.3107a_{46}= -0.64217292 \pm 4.3 \cdot 10^{-7} a47=1.36877108±3.8107a_{47}= -1.36877108 \pm 3.8 \cdot 10^{-7} a48=+0.14433757±1.5107a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7}
a49=+0.49137363±3.7107a_{49}= +0.49137363 \pm 3.7 \cdot 10^{-7} a50=0.25440005±3.3107a_{50}= -0.25440005 \pm 3.3 \cdot 10^{-7} a51=0.46813920±2.8107a_{51}= -0.46813920 \pm 2.8 \cdot 10^{-7}
a52=+0.55421766±4.5107a_{52}= +0.55421766 \pm 4.5 \cdot 10^{-7} a53=1.37827780±5.9107a_{53}= -1.37827780 \pm 5.9 \cdot 10^{-7} a54=0.13608276±1.6107a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7}
a55=+0.77701411±2.8107a_{55}= +0.77701411 \pm 2.8 \cdot 10^{-7} a56=+0.43176580±3.4107a_{56}= +0.43176580 \pm 3.4 \cdot 10^{-7} a57=+1.05042765±6.0107a_{57}= +1.05042765 \pm 6.0 \cdot 10^{-7}
a58=0.39417667±3.3107a_{58}= -0.39417667 \pm 3.3 \cdot 10^{-7} a59=+0.28180059±4.7107a_{59}= +0.28180059 \pm 4.7 \cdot 10^{-7} a60=+0.33662244±3.5107a_{60}= +0.33662244 \pm 3.5 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000