Properties

Label 6.24
Level 66
Weight 00
Character 6.1
Symmetry odd
RR 12.11622
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: 12.1162222939339244410266171732±4101012.1162222939339244410266171732 \pm 4 \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=+1.49666880±9.1108a_{5}= +1.49666880 \pm 9.1 \cdot 10^{-8} a6=0.40824829±1.0108a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8}
a7=+1.41990760±9.0108a_{7}= +1.41990760 \pm 9.0 \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=1.05830466±1.0107a_{10}= -1.05830466 \pm 1.0 \cdot 10^{-7} a11=0.58299700±7.1108a_{11}= -0.58299700 \pm 7.1 \cdot 10^{-8} a12=+0.28867513±5.2108a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8}
a13=0.96665175±1.1107a_{13}= -0.96665175 \pm 1.1 \cdot 10^{-7} a14=1.00402629±1.0107a_{14}= -1.00402629 \pm 1.0 \cdot 10^{-7} a15=+0.86410214±1.0107a_{15}= +0.86410214 \pm 1.0 \cdot 10^{-7}
a16=+0.25a_{16}= +0.25 a17=+1.57590387±7.2108a_{17}= +1.57590387 \pm 7.2 \cdot 10^{-8} a18=0.23570226±7.3108a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8}
a19=+0.41263974±1.5107a_{19}= +0.41263974 \pm 1.5 \cdot 10^{-7} a20=+0.74833440±1.0107a_{20}= +0.74833440 \pm 1.0 \cdot 10^{-7} a21=+0.81978404±1.0107a_{21}= +0.81978404 \pm 1.0 \cdot 10^{-7}
a22=+0.41224113±8.2108a_{22}= +0.41224113 \pm 8.2 \cdot 10^{-8} a23=0.46178627±1.1107a_{23}= -0.46178627 \pm 1.1 \cdot 10^{-7} a24=0.20412415±9.4108a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8}
a25=+1.24001751±8.7108a_{25}= +1.24001751 \pm 8.7 \cdot 10^{-8} a26=+0.68352600±1.2107a_{26}= +0.68352600 \pm 1.2 \cdot 10^{-7} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+0.70995380±1.0107a_{28}= +0.70995380 \pm 1.0 \cdot 10^{-7} a29=1.21125758±8.5108a_{29}= -1.21125758 \pm 8.5 \cdot 10^{-8} a30=0.61101248±1.0107a_{30}= -0.61101248 \pm 1.0 \cdot 10^{-7}
a31=+0.90724731±1.4107a_{31}= +0.90724731 \pm 1.4 \cdot 10^{-7} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=0.33659347±8.2108a_{33}= -0.33659347 \pm 8.2 \cdot 10^{-8}
a34=1.11433231±8.3108a_{34}= -1.11433231 \pm 8.3 \cdot 10^{-8} a35=+2.12513141±7.2108a_{35}= +2.12513141 \pm 7.2 \cdot 10^{-8} a36=+0.16666667±1.0107a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7}
a37=+0.77366380±1.2107a_{37}= +0.77366380 \pm 1.2 \cdot 10^{-7} a38=0.29178036±1.7107a_{38}= -0.29178036 \pm 1.7 \cdot 10^{-7} a39=0.55809665±1.2107a_{39}= -0.55809665 \pm 1.2 \cdot 10^{-7}
a40=0.52915233±1.0107a_{40}= -0.52915233 \pm 1.0 \cdot 10^{-7} a41=0.39182704±6.9108a_{41}= -0.39182704 \pm 6.9 \cdot 10^{-8} a42=0.57967485±1.0107a_{42}= -0.57967485 \pm 1.0 \cdot 10^{-7}
a43=+0.54555449±6.8108a_{43}= +0.54555449 \pm 6.8 \cdot 10^{-8} a44=0.29149850±8.2108a_{44}= -0.29149850 \pm 8.2 \cdot 10^{-8} a45=+0.49888960±1.0107a_{45}= +0.49888960 \pm 1.0 \cdot 10^{-7}
a46=+0.32653220±1.2107a_{46}= +0.32653220 \pm 1.2 \cdot 10^{-7} a47=0.18924609±1.0107a_{47}= -0.18924609 \pm 1.0 \cdot 10^{-7} a48=+0.14433757±1.5107a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7}
a49=+1.01613759±9.9108a_{49}= +1.01613759 \pm 9.9 \cdot 10^{-8} a50=0.87682479±9.8108a_{50}= -0.87682479 \pm 9.8 \cdot 10^{-8} a51=+0.90984852±8.3108a_{51}= +0.90984852 \pm 8.3 \cdot 10^{-8}
a52=0.48332587±1.2107a_{52}= -0.48332587 \pm 1.2 \cdot 10^{-7} a53=0.08160840±1.5107a_{53}= -0.08160840 \pm 1.5 \cdot 10^{-7} a54=0.13608276±1.6107a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7}
a55=0.87255342±7.6108a_{55}= -0.87255342 \pm 7.6 \cdot 10^{-8} a56=0.50201315±1.0107a_{56}= -0.50201315 \pm 1.0 \cdot 10^{-7} a57=+0.23823767±1.7107a_{57}= +0.23823767 \pm 1.7 \cdot 10^{-7}
a58=+0.85648845±9.6108a_{58}= +0.85648845 \pm 9.6 \cdot 10^{-8} a59=1.21904501±1.2107a_{59}= -1.21904501 \pm 1.2 \cdot 10^{-7} a60=+0.43205107±1.0107a_{60}= +0.43205107 \pm 1.0 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000