Properties

Label 15.46
Level 1515
Weight 00
Character 15.1
Symmetry odd
RR 8.485439
Fricke sign +1+1

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Maass form invariants

Level: 15=35 15 = 3 \cdot 5
Weight: 0 0
Character: 15.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 8.4854397033297492137005702893±210108.4854397033297492137005702893 \pm 2 \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=1.17225154±1.0106a_{2}= -1.17225154 \pm 1.0 \cdot 10^{-6} a3=0.57735027±1.0108a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+0.37417368±1.0106a_{4}= +0.37417368 \pm 1.0 \cdot 10^{-6} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=+0.67679974±1.0106a_{6}= +0.67679974 \pm 1.0 \cdot 10^{-6}
a7=1.42437306±9.2107a_{7}= -1.42437306 \pm 9.2 \cdot 10^{-7} a8=+0.73362587±7.7107a_{8}= +0.73362587 \pm 7.7 \cdot 10^{-7} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=+0.52424683±1.0106a_{10}= +0.52424683 \pm 1.0 \cdot 10^{-6} a11=+1.41031972±9.3107a_{11}= +1.41031972 \pm 9.3 \cdot 10^{-7} a12=0.21602928±1.0106a_{12}= -0.21602928 \pm 1.0 \cdot 10^{-6}
a13=+1.41020145±9.2107a_{13}= +1.41020145 \pm 9.2 \cdot 10^{-7} a14=+1.66972351±1.0106a_{14}= +1.66972351 \pm 1.0 \cdot 10^{-6} a15=+0.25819889±1.0108a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8}
a16=1.23416774±8.9107a_{16}= -1.23416774 \pm 8.9 \cdot 10^{-7} a17=1.31860169±8.1107a_{17}= -1.31860169 \pm 8.1 \cdot 10^{-7} a18=0.39075051±1.0106a_{18}= -0.39075051 \pm 1.0 \cdot 10^{-6}
a19=+1.11387576±8.0107a_{19}= +1.11387576 \pm 8.0 \cdot 10^{-7} a20=0.16733556±1.0106a_{20}= -0.16733556 \pm 1.0 \cdot 10^{-6} a21=+0.82236217±9.3107a_{21}= +0.82236217 \pm 9.3 \cdot 10^{-7}
a22=1.65324947±1.1106a_{22}= -1.65324947 \pm 1.1 \cdot 10^{-6} a23=+0.22922865±7.1107a_{23}= +0.22922865 \pm 7.1 \cdot 10^{-7} a24=0.42355909±7.8107a_{24}= -0.42355909 \pm 7.8 \cdot 10^{-7}
a25=+0.2a_{25}= +0.2 a26=1.65311083±1.1106a_{26}= -1.65311083 \pm 1.1 \cdot 10^{-6} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.53296291±1.1106a_{28}= -0.53296291 \pm 1.1 \cdot 10^{-6} a29=1.61169906±5.9107a_{29}= -1.61169906 \pm 5.9 \cdot 10^{-7} a30=0.30267405±1.0106a_{30}= -0.30267405 \pm 1.0 \cdot 10^{-6}
a31=+0.61776986±4.8107a_{31}= +0.61776986 \pm 4.8 \cdot 10^{-7} a32=+0.71312917±8.1107a_{32}= +0.71312917 \pm 8.1 \cdot 10^{-7} a33=0.81424847±9.4107a_{33}= -0.81424847 \pm 9.4 \cdot 10^{-7}
a34=+1.54573286±1.0106a_{34}= +1.54573286 \pm 1.0 \cdot 10^{-6} a35=+0.63699900±9.3107a_{35}= +0.63699900 \pm 9.3 \cdot 10^{-7} a36=+0.12472456±1.0106a_{36}= +0.12472456 \pm 1.0 \cdot 10^{-6}
a37=+0.07025205±6.9107a_{37}= +0.07025205 \pm 6.9 \cdot 10^{-7} a38=1.30574258±9.0107a_{38}= -1.30574258 \pm 9.0 \cdot 10^{-7} a39=0.81418019±9.3107a_{39}= -0.81418019 \pm 9.3 \cdot 10^{-7}
a40=0.32808746±7.8107a_{40}= -0.32808746 \pm 7.8 \cdot 10^{-7} a41=+0.92699518±8.1107a_{41}= +0.92699518 \pm 8.1 \cdot 10^{-7} a42=0.96401532±2.0106a_{42}= -0.96401532 \pm 2.0 \cdot 10^{-6}
a43=0.53247815±8.8107a_{43}= -0.53247815 \pm 8.8 \cdot 10^{-7} a44=+0.52770452±8.7107a_{44}= +0.52770452 \pm 8.7 \cdot 10^{-7} a45=0.14907120±1.4107a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7}
a46=0.26871364±5.3107a_{46}= -0.26871364 \pm 5.3 \cdot 10^{-7} a47=1.32097964±1.0106a_{47}= -1.32097964 \pm 1.0 \cdot 10^{-6} a48=+0.71254708±9.0107a_{48}= +0.71254708 \pm 9.0 \cdot 10^{-7}
a49=+1.02883860±6.9107a_{49}= +1.02883860 \pm 6.9 \cdot 10^{-7} a50=0.23445031±1.0106a_{50}= -0.23445031 \pm 1.0 \cdot 10^{-6} a51=+0.76129504±8.2107a_{51}= +0.76129504 \pm 8.2 \cdot 10^{-7}
a52=+0.52766027±9.5107a_{52}= +0.52766027 \pm 9.5 \cdot 10^{-7} a53=+0.17515534±1.1106a_{53}= +0.17515534 \pm 1.1 \cdot 10^{-6} a54=+0.22559991±1.0106a_{54}= +0.22559991 \pm 1.0 \cdot 10^{-6}
a55=0.63071415±9.4107a_{55}= -0.63071415 \pm 9.4 \cdot 10^{-7} a56=1.04495692±7.9107a_{56}= -1.04495692 \pm 7.9 \cdot 10^{-7} a57=0.64309647±8.1107a_{57}= -0.64309647 \pm 8.1 \cdot 10^{-7}
a58=+1.88931671±7.8107a_{58}= +1.88931671 \pm 7.8 \cdot 10^{-7} a59=0.40724118±7.5107a_{59}= -0.40724118 \pm 7.5 \cdot 10^{-7} a60=+0.09661123±1.0106a_{60}= +0.09661123 \pm 1.0 \cdot 10^{-6}

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