Properties

Label 13.160
Level 1313
Weight 00
Character 13.1
Symmetry even
RR 13.41580
Fricke sign 1-1

Related objects

Downloads

Learn more

Maass form invariants

Level: 13 13
Weight: 0 0
Character: 13.1
Symmetry: even
Fricke sign: 1-1
Spectral parameter: 13.4158009597210121854598159867±210813.4158009597210121854598159867 \pm 2 \cdot 10^{-8}

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=+1.88031464±2.6106a_{2}= +1.88031464 \pm 2.6 \cdot 10^{-6} a3=1.61741644±1.9106a_{3}= -1.61741644 \pm 1.9 \cdot 10^{-6}
a4=+2.53558313±2.8106a_{4}= +2.53558313 \pm 2.8 \cdot 10^{-6} a5=0.24019175±2.1106a_{5}= -0.24019175 \pm 2.1 \cdot 10^{-6} a6=3.04125181±2.5106a_{6}= -3.04125181 \pm 2.5 \cdot 10^{-6}
a7=0.68390253±1.9106a_{7}= -0.68390253 \pm 1.9 \cdot 10^{-6} a8=+2.88737944±2.5106a_{8}= +2.88737944 \pm 2.5 \cdot 10^{-6} a9=+1.61603596±1.7106a_{9}= +1.61603596 \pm 1.7 \cdot 10^{-6}
a10=0.45163606±2.0106a_{10}= -0.45163606 \pm 2.0 \cdot 10^{-6} a11=+1.18549539±1.4106a_{11}= +1.18549539 \pm 1.4 \cdot 10^{-6} a12=4.10109385±2.5106a_{12}= -4.10109385 \pm 2.5 \cdot 10^{-6}
a13=+0.27735010±1.0108a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} a14=1.28595195±2.8106a_{14}= -1.28595195 \pm 2.8 \cdot 10^{-6} a15=+0.38849009±1.6106a_{15}= +0.38849009 \pm 1.6 \cdot 10^{-6}
a16=+2.89359869±1.8106a_{16}= +2.89359869 \pm 1.8 \cdot 10^{-6} a17=1.12199695±1.9106a_{17}= -1.12199695 \pm 1.9 \cdot 10^{-6} a18=+3.03865606±2.0106a_{18}= +3.03865606 \pm 2.0 \cdot 10^{-6}
a19=1.83018630±2.1106a_{19}= -1.83018630 \pm 2.1 \cdot 10^{-6} a20=0.60902615±2.4106a_{20}= -0.60902615 \pm 2.4 \cdot 10^{-6} a21=+1.10615521±1.6106a_{21}= +1.10615521 \pm 1.6 \cdot 10^{-6}
a22=+2.22910433±1.4106a_{22}= +2.22910433 \pm 1.4 \cdot 10^{-6} a23=0.64541876±1.4106a_{23}= -0.64541876 \pm 1.4 \cdot 10^{-6} a24=4.67009499±2.3106a_{24}= -4.67009499 \pm 2.3 \cdot 10^{-6}
a25=0.94230792±2.4106a_{25}= -0.94230792 \pm 2.4 \cdot 10^{-6} a26=+0.52150545±2.6106a_{26}= +0.52150545 \pm 2.6 \cdot 10^{-6} a27=0.99638669±2.1106a_{27}= -0.99638669 \pm 2.1 \cdot 10^{-6}
a28=1.73409173±3.0106a_{28}= -1.73409173 \pm 3.0 \cdot 10^{-6} a29=+0.87752768±1.8106a_{29}= +0.87752768 \pm 1.8 \cdot 10^{-6} a30=+0.73048360±1.3106a_{30}= +0.73048360 \pm 1.3 \cdot 10^{-6}
a31=0.60009031±1.4106a_{31}= -0.60009031 \pm 1.4 \cdot 10^{-6} a32=+2.55349652±1.9106a_{32}= +2.55349652 \pm 1.9 \cdot 10^{-6} a33=1.91743974±1.7106a_{33}= -1.91743974 \pm 1.7 \cdot 10^{-6}
a34=2.10970728±2.4106a_{34}= -2.10970728 \pm 2.4 \cdot 10^{-6} a35=+0.16426775±1.8106a_{35}= +0.16426775 \pm 1.8 \cdot 10^{-6} a36=+4.09759351±1.7106a_{36}= +4.09759351 \pm 1.7 \cdot 10^{-6}
a37=0.64629534±1.7106a_{37}= -0.64629534 \pm 1.7 \cdot 10^{-6} a38=3.44132608±2.8106a_{38}= -3.44132608 \pm 2.8 \cdot 10^{-6} a39=0.44859061±2.0106a_{39}= -0.44859061 \pm 2.0 \cdot 10^{-6}
a40=0.69352472±2.3106a_{40}= -0.69352472 \pm 2.3 \cdot 10^{-6} a41=1.17413876±2.9106a_{41}= -1.17413876 \pm 2.9 \cdot 10^{-6} a42=+2.07991982±2.3106a_{42}= +2.07991982 \pm 2.3 \cdot 10^{-6}
a43=+0.27150214±1.6106a_{43}= +0.27150214 \pm 1.6 \cdot 10^{-6} a44=+3.00592211±1.1106a_{44}= +3.00592211 \pm 1.1 \cdot 10^{-6} a45=0.38815850±1.5106a_{45}= -0.38815850 \pm 1.5 \cdot 10^{-6}
a46=1.21359034±1.7106a_{46}= -1.21359034 \pm 1.7 \cdot 10^{-6} a47=+0.30525552±1.5106a_{47}= +0.30525552 \pm 1.5 \cdot 10^{-6} a48=4.68015410±1.6106a_{48}= -4.68015410 \pm 1.6 \cdot 10^{-6}
a49=0.53227732±1.5106a_{49}= -0.53227732 \pm 1.5 \cdot 10^{-6} a50=1.77183538±1.9106a_{50}= -1.77183538 \pm 1.9 \cdot 10^{-6} a51=+1.81473631±2.1106a_{51}= +1.81473631 \pm 2.1 \cdot 10^{-6}
a52=+0.70324423±2.8106a_{52}= +0.70324423 \pm 2.8 \cdot 10^{-6} a53=0.91096385±2.1106a_{53}= -0.91096385 \pm 2.1 \cdot 10^{-6} a54=1.87352047±2.2106a_{54}= -1.87352047 \pm 2.2 \cdot 10^{-6}
a55=0.28474621±1.4106a_{55}= -0.28474621 \pm 1.4 \cdot 10^{-6} a56=1.97468612±2.4106a_{56}= -1.97468612 \pm 2.4 \cdot 10^{-6} a57=+2.96017341±1.1106a_{57}= +2.96017341 \pm 1.1 \cdot 10^{-6}
a58=+1.65002814±3.0106a_{58}= +1.65002814 \pm 3.0 \cdot 10^{-6} a59=1.37046961±1.7106a_{59}= -1.37046961 \pm 1.7 \cdot 10^{-6} a60=+0.98504891±1.5106a_{60}= +0.98504891 \pm 1.5 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000