Properties

Label 15.16
Level 1515
Weight 00
Character 15.1
Symmetry odd
RR 5.046391
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: 5.04639152421925115467652117489±210115.04639152421925115467652117489 \pm 2 \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=+1.12638288±4.1108a_{2}= +1.12638288 \pm 4.1 \cdot 10^{-8} a3=0.57735027±1.0108a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+0.26873840±4.1108a_{4}= +0.26873840 \pm 4.1 \cdot 10^{-8} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=0.65031746±5.2108a_{6}= -0.65031746 \pm 5.2 \cdot 10^{-8}
a7=1.67990027±3.6108a_{7}= -1.67990027 \pm 3.6 \cdot 10^{-8} a8=0.82368055±3.0108a_{8}= -0.82368055 \pm 3.0 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.50373374±5.2108a_{10}= -0.50373374 \pm 5.2 \cdot 10^{-8} a11=+1.33584752±3.6108a_{11}= +1.33584752 \pm 3.6 \cdot 10^{-8} a12=0.15515618±5.2108a_{12}= -0.15515618 \pm 5.2 \cdot 10^{-8}
a13=0.39969907±3.5108a_{13}= -0.39969907 \pm 3.5 \cdot 10^{-8} a14=1.89221091±4.2108a_{14}= -1.89221091 \pm 4.2 \cdot 10^{-8} a15=+0.25819889±1.0108a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8}
a16=1.19651807±3.5108a_{16}= -1.19651807 \pm 3.5 \cdot 10^{-8} a17=+0.92225614±3.1108a_{17}= +0.92225614 \pm 3.1 \cdot 10^{-8} a18=+0.37546096±5.2108a_{18}= +0.37546096 \pm 5.2 \cdot 10^{-8}
a19=0.48241875±3.1108a_{19}= -0.48241875 \pm 3.1 \cdot 10^{-8} a20=0.12018346±5.2108a_{20}= -0.12018346 \pm 5.2 \cdot 10^{-8} a21=+0.96989087±4.6108a_{21}= +0.96989087 \pm 4.6 \cdot 10^{-8}
a22=+1.50467578±4.3108a_{22}= +1.50467578 \pm 4.3 \cdot 10^{-8} a23=1.47555439±2.7108a_{23}= -1.47555439 \pm 2.7 \cdot 10^{-8} a24=+0.47555219±4.0108a_{24}= +0.47555219 \pm 4.0 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=0.45021419±4.6108a_{26}= -0.45021419 \pm 4.6 \cdot 10^{-8} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.45145370±4.6108a_{28}= -0.45145370 \pm 4.6 \cdot 10^{-8} a29=0.57607064±2.3108a_{29}= -0.57607064 \pm 2.3 \cdot 10^{-8} a30=+0.29083081±5.2108a_{30}= +0.29083081 \pm 5.2 \cdot 10^{-8}
a31=+0.03412613±1.8108a_{31}= +0.03412613 \pm 1.8 \cdot 10^{-8} a32=0.52405692±3.1108a_{32}= -0.52405692 \pm 3.1 \cdot 10^{-8} a33=0.77125192±4.6108a_{33}= -0.77125192 \pm 4.6 \cdot 10^{-8}
a34=+1.03881353±3.9108a_{34}= +1.03881353 \pm 3.9 \cdot 10^{-8} a35=+0.75127424±4.6108a_{35}= +0.75127424 \pm 4.6 \cdot 10^{-8} a36=+0.08957947±5.2108a_{36}= +0.08957947 \pm 5.2 \cdot 10^{-8}
a37=0.15244083±2.7108a_{37}= -0.15244083 \pm 2.7 \cdot 10^{-8} a38=0.54338823±3.5108a_{38}= -0.54338823 \pm 3.5 \cdot 10^{-8} a39=+0.23076637±4.6108a_{39}= +0.23076637 \pm 4.6 \cdot 10^{-8}
a40=+0.36836114±4.0108a_{40}= +0.36836114 \pm 4.0 \cdot 10^{-8} a41=0.20874690±3.1108a_{41}= -0.20874690 \pm 3.1 \cdot 10^{-8} a42=+1.09246848±8.8108a_{42}= +1.09246848 \pm 8.8 \cdot 10^{-8}
a43=0.32873533±3.4108a_{43}= -0.32873533 \pm 3.4 \cdot 10^{-8} a44=+0.35899352±3.4108a_{44}= +0.35899352 \pm 3.4 \cdot 10^{-8} a45=0.14907120±1.4107a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7}
a46=1.66203920±2.0108a_{46}= -1.66203920 \pm 2.0 \cdot 10^{-8} a47=0.29840022±4.1108a_{47}= -0.29840022 \pm 4.1 \cdot 10^{-8} a48=+0.69081003±4.5108a_{48}= +0.69081003 \pm 4.5 \cdot 10^{-8}
a49=+1.82206492±2.7108a_{49}= +1.82206492 \pm 2.7 \cdot 10^{-8} a50=+0.22527658±5.2108a_{50}= +0.22527658 \pm 5.2 \cdot 10^{-8} a51=0.53246483±4.2108a_{51}= -0.53246483 \pm 4.2 \cdot 10^{-8}
a52=0.10741449±3.7108a_{52}= -0.10741449 \pm 3.7 \cdot 10^{-8} a53=1.76867867±4.4108a_{53}= -1.76867867 \pm 4.4 \cdot 10^{-8} a54=0.21677249±5.2108a_{54}= -0.21677249 \pm 5.2 \cdot 10^{-8}
a55=0.59740917±4.6108a_{55}= -0.59740917 \pm 4.6 \cdot 10^{-8} a56=+1.38370119±3.1108a_{56}= +1.38370119 \pm 3.1 \cdot 10^{-8} a57=+0.27852460±4.2108a_{57}= +0.27852460 \pm 4.2 \cdot 10^{-8}
a58=0.64887611±3.0108a_{58}= -0.64887611 \pm 3.0 \cdot 10^{-8} a59=0.26592633±2.9108a_{59}= -0.26592633 \pm 2.9 \cdot 10^{-8} a60=+0.06938796±5.2108a_{60}= +0.06938796 \pm 5.2 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000