Properties

Label 6.10
Level 66
Weight 00
Character 6.1
Symmetry even
RR 7.386274
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: 7.38627450581586415779132114734±210127.38627450581586415779132114734 \pm 2 \cdot 10^{-12}

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=0.09856581±1108a_{5}= -0.09856581 \pm 1 \cdot 10^{-8} a6=0.40824829±1.0108a_{6}= -0.40824829 \pm 1.0 \cdot 10^{-8}
a7=1.48570553±1108a_{7}= -1.48570553 \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=+0.06969655±1.0108a_{10}= +0.06969655 \pm 1.0 \cdot 10^{-8} a11=0.99923097±1108a_{11}= -0.99923097 \pm 1 \cdot 10^{-8} a12=+0.28867513±5.2108a_{12}= +0.28867513 \pm 5.2 \cdot 10^{-8}
a13=1.34679465±1108a_{13}= -1.34679465 \pm 1 \cdot 10^{-8} a14=+1.05055246±1.0108a_{14}= +1.05055246 \pm 1.0 \cdot 10^{-8} a15=0.05690700±1.0108a_{15}= -0.05690700 \pm 1.0 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=+0.73419593±1108a_{17}= +0.73419593 \pm 1 \cdot 10^{-8} a18=0.23570226±7.3108a_{18}= -0.23570226 \pm 7.3 \cdot 10^{-8}
a19=1.13410256±1108a_{19}= -1.13410256 \pm 1 \cdot 10^{-8} a20=0.04928290±1.0108a_{20}= -0.04928290 \pm 1.0 \cdot 10^{-8} a21=0.85777249±1.0108a_{21}= -0.85777249 \pm 1.0 \cdot 10^{-8}
a22=+0.70656300±1.0108a_{22}= +0.70656300 \pm 1.0 \cdot 10^{-8} a23=+1.36320691±1108a_{23}= +1.36320691 \pm 1 \cdot 10^{-8} a24=0.20412415±9.4108a_{24}= -0.20412415 \pm 9.4 \cdot 10^{-8}
a25=0.99028478±1108a_{25}= -0.99028478 \pm 1 \cdot 10^{-8} a26=+0.95232763±1.0108a_{26}= +0.95232763 \pm 1.0 \cdot 10^{-8} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.74285277±1.0108a_{28}= -0.74285277 \pm 1.0 \cdot 10^{-8} a29=0.14358963±1108a_{29}= -0.14358963 \pm 1 \cdot 10^{-8} a30=+0.04023932±1.0108a_{30}= +0.04023932 \pm 1.0 \cdot 10^{-8}
a31=+0.36973412±1108a_{31}= +0.36973412 \pm 1 \cdot 10^{-8} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=0.57690627±1.0108a_{33}= -0.57690627 \pm 1.0 \cdot 10^{-8}
a34=0.51915492±1.0108a_{34}= -0.51915492 \pm 1.0 \cdot 10^{-8} a35=+0.14643977±1108a_{35}= +0.14643977 \pm 1 \cdot 10^{-8} a36=+0.16666667±1.0107a_{36}= +0.16666667 \pm 1.0 \cdot 10^{-7}
a37=+1.25626416±1108a_{37}= +1.25626416 \pm 1 \cdot 10^{-8} a38=+0.80193161±1.0108a_{38}= +0.80193161 \pm 1.0 \cdot 10^{-8} a39=0.77757225±1.0108a_{39}= -0.77757225 \pm 1.0 \cdot 10^{-8}
a40=+0.03484828±1.0108a_{40}= +0.03484828 \pm 1.0 \cdot 10^{-8} a41=0.15258651±1108a_{41}= -0.15258651 \pm 1 \cdot 10^{-8} a42=+0.60653674±1.0108a_{42}= +0.60653674 \pm 1.0 \cdot 10^{-8}
a43=0.89399174±1108a_{43}= -0.89399174 \pm 1 \cdot 10^{-8} a44=0.49961549±1.0108a_{44}= -0.49961549 \pm 1.0 \cdot 10^{-8} a45=0.03285527±1.0108a_{45}= -0.03285527 \pm 1.0 \cdot 10^{-8}
a46=0.96393285±1.0108a_{46}= -0.96393285 \pm 1.0 \cdot 10^{-8} a47=0.27761026±1108a_{47}= -0.27761026 \pm 1 \cdot 10^{-8} a48=+0.14433757±1.5107a_{48}= +0.14433757 \pm 1.5 \cdot 10^{-7}
a49=+1.20732093±1108a_{49}= +1.20732093 \pm 1 \cdot 10^{-8} a50=+0.70023708±1.0108a_{50}= +0.70023708 \pm 1.0 \cdot 10^{-8} a51=+0.42388822±1.0108a_{51}= +0.42388822 \pm 1.0 \cdot 10^{-8}
a52=0.67339732±1.0108a_{52}= -0.67339732 \pm 1.0 \cdot 10^{-8} a53=+0.58777932±1108a_{53}= +0.58777932 \pm 1 \cdot 10^{-8} a54=0.13608276±1.6107a_{54}= -0.13608276 \pm 1.6 \cdot 10^{-7}
a55=+0.09849001±1108a_{55}= +0.09849001 \pm 1 \cdot 10^{-8} a56=+0.52527623±1.0108a_{56}= +0.52527623 \pm 1.0 \cdot 10^{-8} a57=0.65477442±1.0108a_{57}= -0.65477442 \pm 1.0 \cdot 10^{-8}
a58=+0.10153320±1.0108a_{58}= +0.10153320 \pm 1.0 \cdot 10^{-8} a59=1.64298114±1108a_{59}= -1.64298114 \pm 1 \cdot 10^{-8} a60=0.02845350±1.0108a_{60}= -0.02845350 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000