Properties

Label 6.43
Level 66
Weight 00
Character 6.1
Symmetry odd
RR 16.13506
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: 16.1350656626952838892792751054±410716.1350656626952838892792751054 \pm 4 \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=+1.11804145±4.3104a_{5}= +1.11804145 \pm 4.3 \cdot 10^{-4} a6=0.40824829±1.0108a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8}
a7=+1.57650130±4.3104a_{7}= +1.57650130 \pm 4.3 \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=+0.79057469±4.3104a_{10}= +0.79057469 \pm 4.3 \cdot 10^{-4} a11=0.54859093±3.4104a_{11}= -0.54859093 \pm 3.4 \cdot 10^{-4} a12=0.28867513±5.2108a_{12}= -0.28867513 \pm 5.2 \cdot 10^{-8}
a13=1.48076976±5.6104a_{13}= -1.48076976 \pm 5.6 \cdot 10^{-4} a14=+1.11475476±4.3104a_{14}= +1.11475476 \pm 4.3 \cdot 10^{-4} a15=0.64550153±4.3104a_{15}= -0.64550153 \pm 4.3 \cdot 10^{-4}
a16=+0.25a_{16}= +0.25 a17=+0.83954495±3.4104a_{17}= +0.83954495 \pm 3.4 \cdot 10^{-4} a18=+0.23570226±7.3108a_{18}= +0.23570226 \pm 7.3 \cdot 10^{-8}
a19=+1.46995620±7.6104a_{19}= +1.46995620 \pm 7.6 \cdot 10^{-4} a20=+0.55902072±4.3104a_{20}= +0.55902072 \pm 4.3 \cdot 10^{-4} a21=0.91019345±4.3104a_{21}= -0.91019345 \pm 4.3 \cdot 10^{-4}
a22=0.38791237±3.4104a_{22}= -0.38791237 \pm 3.4 \cdot 10^{-4} a23=0.18937809±5.4104a_{23}= -0.18937809 \pm 5.4 \cdot 10^{-4} a24=0.20412415±9.4108a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8}
a25=+0.25001667±4.2104a_{25}= +0.25001667 \pm 4.2 \cdot 10^{-4} a26=1.04706234±5.6104a_{26}= -1.04706234 \pm 5.6 \cdot 10^{-4} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+0.78825065±4.3104a_{28}= +0.78825065 \pm 4.3 \cdot 10^{-4} a29=+1.46575056±4.0104a_{29}= +1.46575056 \pm 4.0 \cdot 10^{-4} a30=0.45643851±4.3104a_{30}= -0.45643851 \pm 4.3 \cdot 10^{-4}
a31=+0.03377559±7.0104a_{31}= +0.03377559 \pm 7.0 \cdot 10^{-4} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=+0.31672912±3.4104a_{33}= +0.31672912 \pm 3.4 \cdot 10^{-4}
a34=+0.59364793±3.4104a_{34}= +0.59364793 \pm 3.4 \cdot 10^{-4} a35=+1.76259379±3.4104a_{35}= +1.76259379 \pm 3.4 \cdot 10^{-4} a36=+0.16666667±1.0107a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7}
a37=+0.00310624±6.0104a_{37}= +0.00310624 \pm 6.0 \cdot 10^{-4} a38=+1.03941600±7.6104a_{38}= +1.03941600 \pm 7.6 \cdot 10^{-4} a39=+0.85492282±5.6104a_{39}= +0.85492282 \pm 5.6 \cdot 10^{-4}
a40=+0.39528734±4.3104a_{40}= +0.39528734 \pm 4.3 \cdot 10^{-4} a41=0.90020675±3.2104a_{41}= -0.90020675 \pm 3.2 \cdot 10^{-4} a42=0.64360396±4.3104a_{42}= -0.64360396 \pm 4.3 \cdot 10^{-4}
a43=+1.41185778±3.2104a_{43}= +1.41185778 \pm 3.2 \cdot 10^{-4} a44=0.27429547±3.4104a_{44}= -0.27429547 \pm 3.4 \cdot 10^{-4} a45=+0.37268048±4.3104a_{45}= +0.37268048 \pm 4.3 \cdot 10^{-4}
a46=0.13391053±5.4104a_{46}= -0.13391053 \pm 5.4 \cdot 10^{-4} a47=+0.69758544±4.9104a_{47}= +0.69758544 \pm 4.9 \cdot 10^{-4} a48=0.14433757±1.5107a_{48}= -0.14433757 \pm 1.5 \cdot 10^{-7}
a49=+1.48535634±4.7104a_{49}= +1.48535634 \pm 4.7 \cdot 10^{-4} a50=+0.17678849±4.2104a_{50}= +0.17678849 \pm 4.2 \cdot 10^{-4} a51=0.48471150±3.4104a_{51}= -0.48471150 \pm 3.4 \cdot 10^{-4}
a52=0.74038488±5.6104a_{52}= -0.74038488 \pm 5.6 \cdot 10^{-4} a53=0.03577334±7.5104a_{53}= -0.03577334 \pm 7.5 \cdot 10^{-4} a54=0.13608276±1.6107a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7}
a55=0.61334740±3.6104a_{55}= -0.61334740 \pm 3.6 \cdot 10^{-4} a56=+0.55737738±4.3104a_{56}= +0.55737738 \pm 4.3 \cdot 10^{-4} a57=0.84867961±7.6104a_{57}= -0.84867961 \pm 7.6 \cdot 10^{-4}
a58=+1.03644216±4.0104a_{58}= +1.03644216 \pm 4.0 \cdot 10^{-4} a59=0.23452108±6.0104a_{59}= -0.23452108 \pm 6.0 \cdot 10^{-4} a60=0.32275076±4.3104a_{60}= -0.32275076 \pm 4.3 \cdot 10^{-4}

Displaying ana_n with nn up to: 60 180 1000