Properties

Label 10.23
Level 1010
Weight 00
Character 10.1
Symmetry odd
RR 8.423388
Fricke sign 1-1

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Maass form invariants

Level: 10=25 10 = 2 \cdot 5
Weight: 0 0
Character: 10.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 8.42338862094813782250280224667±210118.42338862094813782250280224667 \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=0.70710678±1.0108a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} a3=0.14911412±1108a_{3}= -0.14911412 \pm 1 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=+0.44721360±1.0108a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} a6=+0.10543961±1.4108a_{6}= +0.10543961 \pm 1.4 \cdot 10^{-8}
a7=1.32642196±1108a_{7}= -1.32642196 \pm 1 \cdot 10^{-8} a8=0.35355339±4.2108a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} a9=0.97776498±1108a_{9}= -0.97776498 \pm 1 \cdot 10^{-8}
a10=0.31622777±1.0108a_{10}= -0.31622777 \pm 1.0 \cdot 10^{-8} a11=+1.67605934±1108a_{11}= +1.67605934 \pm 1 \cdot 10^{-8} a12=0.07455706±1.4108a_{12}= -0.07455706 \pm 1.4 \cdot 10^{-8}
a13=0.57506067±1108a_{13}= -0.57506067 \pm 1 \cdot 10^{-8} a14=+0.93792196±1.5108a_{14}= +0.93792196 \pm 1.5 \cdot 10^{-8} a15=0.06668586±1.4108a_{15}= -0.06668586 \pm 1.4 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=+1.37759571±1108a_{17}= +1.37759571 \pm 1 \cdot 10^{-8} a18=+0.69138425±1.4108a_{18}= +0.69138425 \pm 1.4 \cdot 10^{-8}
a19=+0.52860462±1108a_{19}= +0.52860462 \pm 1 \cdot 10^{-8} a20=+0.22360680±8.4108a_{20}= +0.22360680 \pm 8.4 \cdot 10^{-8} a21=+0.19778825±1108a_{21}= +0.19778825 \pm 1 \cdot 10^{-8}
a22=1.18515292±1.4108a_{22}= -1.18515292 \pm 1.4 \cdot 10^{-8} a23=+0.04410534±1108a_{23}= +0.04410534 \pm 1 \cdot 10^{-8} a24=+0.05271980±1.4108a_{24}= +0.05271980 \pm 1.4 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=+0.40662930±1.5108a_{26}= +0.40662930 \pm 1.5 \cdot 10^{-8} a27=+0.29491269±1108a_{27}= +0.29491269 \pm 1 \cdot 10^{-8}
a28=0.66321098±1.5108a_{28}= -0.66321098 \pm 1.5 \cdot 10^{-8} a29=+1.30709968±1108a_{29}= +1.30709968 \pm 1 \cdot 10^{-8} a30=+0.04715403±1.4108a_{30}= +0.04715403 \pm 1.4 \cdot 10^{-8}
a31=+0.61019073±1108a_{31}= +0.61019073 \pm 1 \cdot 10^{-8} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=0.24992412±1108a_{33}= -0.24992412 \pm 1 \cdot 10^{-8}
a34=0.97410727±1.3108a_{34}= -0.97410727 \pm 1.3 \cdot 10^{-8} a35=0.59319393±1.5108a_{35}= -0.59319393 \pm 1.5 \cdot 10^{-8} a36=0.48888249±1.4108a_{36}= -0.48888249 \pm 1.4 \cdot 10^{-8}
a37=+1.43214181±1108a_{37}= +1.43214181 \pm 1 \cdot 10^{-8} a38=0.37377991±1.4108a_{38}= -0.37377991 \pm 1.4 \cdot 10^{-8} a39=+0.08574967±1108a_{39}= +0.08574967 \pm 1 \cdot 10^{-8}
a40=0.15811388±1.2107a_{40}= -0.15811388 \pm 1.2 \cdot 10^{-7} a41=+0.23082620±1108a_{41}= +0.23082620 \pm 1 \cdot 10^{-8} a42=0.13985741±1.9108a_{42}= -0.13985741 \pm 1.9 \cdot 10^{-8}
a43=0.18740678±1108a_{43}= -0.18740678 \pm 1 \cdot 10^{-8} a44=+0.83802967±1.4108a_{44}= +0.83802967 \pm 1.4 \cdot 10^{-8} a45=0.43726979±1.4108a_{45}= -0.43726979 \pm 1.4 \cdot 10^{-8}
a46=0.03118719±1.6108a_{46}= -0.03118719 \pm 1.6 \cdot 10^{-8} a47=+0.51320320±1108a_{47}= +0.51320320 \pm 1 \cdot 10^{-8} a48=0.03727853±1.4108a_{48}= -0.03727853 \pm 1.4 \cdot 10^{-8}
a49=+0.75939522±1108a_{49}= +0.75939522 \pm 1 \cdot 10^{-8} a50=0.14142136±1.5107a_{50}= -0.14142136 \pm 1.5 \cdot 10^{-7} a51=0.20541898±1108a_{51}= -0.20541898 \pm 1 \cdot 10^{-8}
a52=0.28753033±1.5108a_{52}= -0.28753033 \pm 1.5 \cdot 10^{-8} a53=1.14453758±1108a_{53}= -1.14453758 \pm 1 \cdot 10^{-8} a54=0.20853476±1.5108a_{54}= -0.20853476 \pm 1.5 \cdot 10^{-8}
a55=+0.74955652±1.4108a_{55}= +0.74955652 \pm 1.4 \cdot 10^{-8} a56=+0.46896098±1.5108a_{56}= +0.46896098 \pm 1.5 \cdot 10^{-8} a57=0.07882241±1108a_{57}= -0.07882241 \pm 1 \cdot 10^{-8}
a58=0.92425905±1.7108a_{58}= -0.92425905 \pm 1.7 \cdot 10^{-8} a59=1.25066459±1108a_{59}= -1.25066459 \pm 1 \cdot 10^{-8} a60=0.03334293±1.4108a_{60}= -0.03334293 \pm 1.4 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000