Properties

Label 15.22
Level 1515
Weight 00
Character 15.1
Symmetry even
RR 5.859504
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: even
Fricke sign: 1-1
Spectral parameter: 5.85950414296348633115912355467±210115.85950414296348633115912355467 \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=1.49233525±1108a_{2}= -1.49233525 \pm 1 \cdot 10^{-8} a3=0.57735027±1.0108a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+1.22706450±1108a_{4}= +1.22706450 \pm 1 \cdot 10^{-8} a5=+0.44721360±1.0108a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} a6=+0.86160016±1.0108a_{6}= +0.86160016 \pm 1.0 \cdot 10^{-8}
a7=+0.43506977±1108a_{7}= +0.43506977 \pm 1 \cdot 10^{-8} a8=0.33885636±1108a_{8}= -0.33885636 \pm 1 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.66739261±1.0108a_{10}= -0.66739261 \pm 1.0 \cdot 10^{-8} a11=1.45351474±1108a_{11}= -1.45351474 \pm 1 \cdot 10^{-8} a12=0.70844602±1.0108a_{12}= -0.70844602 \pm 1.0 \cdot 10^{-8}
a13=+1.43663049±1108a_{13}= +1.43663049 \pm 1 \cdot 10^{-8} a14=0.64926995±1108a_{14}= -0.64926995 \pm 1 \cdot 10^{-8} a15=0.25819889±1.0108a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8}
a16=0.72137721±1108a_{16}= -0.72137721 \pm 1 \cdot 10^{-8} a17=+0.12264391±1108a_{17}= +0.12264391 \pm 1 \cdot 10^{-8} a18=0.49744508±1.0108a_{18}= -0.49744508 \pm 1.0 \cdot 10^{-8}
a19=0.11950906±1108a_{19}= -0.11950906 \pm 1 \cdot 10^{-8} a20=+0.54875993±1.0108a_{20}= +0.54875993 \pm 1.0 \cdot 10^{-8} a21=0.25118765±1.0108a_{21}= -0.25118765 \pm 1.0 \cdot 10^{-8}
a22=+2.16913128±1108a_{22}= +2.16913128 \pm 1 \cdot 10^{-8} a23=1.50557738±1108a_{23}= -1.50557738 \pm 1 \cdot 10^{-8} a24=+0.19563881±1.0108a_{24}= +0.19563881 \pm 1.0 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=2.14393433±1108a_{26}= -2.14393433 \pm 1 \cdot 10^{-8} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+0.53385867±1108a_{28}= +0.53385867 \pm 1 \cdot 10^{-8} a29=1.46699387±1108a_{29}= -1.46699387 \pm 1 \cdot 10^{-8} a30=+0.38531931±1.0108a_{30}= +0.38531931 \pm 1.0 \cdot 10^{-8}
a31=+0.42825837±1108a_{31}= +0.42825837 \pm 1 \cdot 10^{-8} a32=+1.41539300±1108a_{32}= +1.41539300 \pm 1 \cdot 10^{-8} a33=+0.83918712±1.0108a_{33}= +0.83918712 \pm 1.0 \cdot 10^{-8}
a34=0.18302583±1108a_{34}= -0.18302583 \pm 1 \cdot 10^{-8} a35=+0.19456911±1.0108a_{35}= +0.19456911 \pm 1.0 \cdot 10^{-8} a36=+0.40902150±1.0108a_{36}= +0.40902150 \pm 1.0 \cdot 10^{-8}
a37=+0.32724539±1108a_{37}= +0.32724539 \pm 1 \cdot 10^{-8} a38=+0.17834758±1108a_{38}= +0.17834758 \pm 1 \cdot 10^{-8} a39=0.82943900±1.0108a_{39}= -0.82943900 \pm 1.0 \cdot 10^{-8}
a40=0.15154117±1.0108a_{40}= -0.15154117 \pm 1.0 \cdot 10^{-8} a41=0.50373965±1108a_{41}= -0.50373965 \pm 1 \cdot 10^{-8} a42=+0.37485618±1.1108a_{42}= +0.37485618 \pm 1.1 \cdot 10^{-8}
a43=1.56281428±1108a_{43}= -1.56281428 \pm 1 \cdot 10^{-8} a44=1.78355634±1108a_{44}= -1.78355634 \pm 1 \cdot 10^{-8} a45=+0.14907120±1.4107a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7}
a46=+2.24682619±1108a_{46}= +2.24682619 \pm 1 \cdot 10^{-8} a47=0.90218632±1108a_{47}= -0.90218632 \pm 1 \cdot 10^{-8} a48=+0.41648733±1.0108a_{48}= +0.41648733 \pm 1.0 \cdot 10^{-8}
a49=0.81071430±1108a_{49}= -0.81071430 \pm 1 \cdot 10^{-8} a50=0.29846705±1.0108a_{50}= -0.29846705 \pm 1.0 \cdot 10^{-8} a51=0.07080849±1.0108a_{51}= -0.07080849 \pm 1.0 \cdot 10^{-8}
a52=+1.76283828±1108a_{52}= +1.76283828 \pm 1 \cdot 10^{-8} a53=+1.30016658±1108a_{53}= +1.30016658 \pm 1 \cdot 10^{-8} a54=+0.28720005±1.0108a_{54}= +0.28720005 \pm 1.0 \cdot 10^{-8}
a55=0.65003155±1.0108a_{55}= -0.65003155 \pm 1.0 \cdot 10^{-8} a56=0.14742616±1108a_{56}= -0.14742616 \pm 1 \cdot 10^{-8} a57=+0.06899859±1.0108a_{57}= +0.06899859 \pm 1.0 \cdot 10^{-8}
a58=+2.18924666±1108a_{58}= +2.18924666 \pm 1 \cdot 10^{-8} a59=0.87399392±1108a_{59}= -0.87399392 \pm 1 \cdot 10^{-8} a60=0.31682669±1.0108a_{60}= -0.31682669 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000