Properties

Label 13.157
Level 1313
Weight 00
Character 13.1
Symmetry odd
RR 13.35820
Fricke sign 1-1

Related objects

Downloads

Learn more

Maass form invariants

Level: 13 13
Weight: 0 0
Character: 13.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 13.3582067458369704833518679994±410813.3582067458369704833518679994 \pm 4 \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=0.80423950±1.5104a_{2}= -0.80423950 \pm 1.5 \cdot 10^{-4} a3=+0.67317451±1.4104a_{3}= +0.67317451 \pm 1.4 \cdot 10^{-4}
a4=0.35319882±1.3104a_{4}= -0.35319882 \pm 1.3 \cdot 10^{-4} a5=+0.27788527±1.3104a_{5}= +0.27788527 \pm 1.3 \cdot 10^{-4} a6=0.54139354±1.6104a_{6}= -0.54139354 \pm 1.6 \cdot 10^{-4}
a7=1.26715774±1.3104a_{7}= -1.26715774 \pm 1.3 \cdot 10^{-4} a8=+1.08829595±1.1104a_{8}= +1.08829595 \pm 1.1 \cdot 10^{-4} a9=0.54683607±1.4104a_{9}= -0.54683607 \pm 1.4 \cdot 10^{-4}
a10=0.22348632±1.4104a_{10}= -0.22348632 \pm 1.4 \cdot 10^{-4} a11=1.29891987±1.2104a_{11}= -1.29891987 \pm 1.2 \cdot 10^{-4} a12=0.23776444±1.4104a_{12}= -0.23776444 \pm 1.4 \cdot 10^{-4}
a13=+0.27735010±1.0108a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} a14=+1.01909832±1.4104a_{14}= +1.01909832 \pm 1.4 \cdot 10^{-4} a15=+0.18706528±1.5104a_{15}= +0.18706528 \pm 1.5 \cdot 10^{-4}
a16=0.52205177±1.2104a_{16}= -0.52205177 \pm 1.2 \cdot 10^{-4} a17=0.09971520±1.3104a_{17}= -0.09971520 \pm 1.3 \cdot 10^{-4} a18=+0.43978717±1.6104a_{18}= +0.43978717 \pm 1.6 \cdot 10^{-4}
a19=+0.98390521±1.1104a_{19}= +0.98390521 \pm 1.1 \cdot 10^{-4} a20=0.09814875±1.3104a_{20}= -0.09814875 \pm 1.3 \cdot 10^{-4} a21=0.85301830±1.1104a_{21}= -0.85301830 \pm 1.1 \cdot 10^{-4}
a22=+1.04464267±1.3104a_{22}= +1.04464267 \pm 1.3 \cdot 10^{-4} a23=0.60576610±1.1104a_{23}= -0.60576610 \pm 1.1 \cdot 10^{-4} a24=+0.73261310±1.1104a_{24}= +0.73261310 \pm 1.1 \cdot 10^{-4}
a25=0.92277977±1.0104a_{25}= -0.92277977 \pm 1.0 \cdot 10^{-4} a26=0.22305591±1.5104a_{26}= -0.22305591 \pm 1.5 \cdot 10^{-4} a27=1.04129062±1.1104a_{27}= -1.04129062 \pm 1.1 \cdot 10^{-4}
a28=+0.44755862±1.2104a_{28}= +0.44755862 \pm 1.2 \cdot 10^{-4} a29=+0.80154077±1.0104a_{29}= +0.80154077 \pm 1.0 \cdot 10^{-4} a30=0.15044529±1.9104a_{30}= -0.15044529 \pm 1.9 \cdot 10^{-4}
a31=1.57670479±1.4104a_{31}= -1.57670479 \pm 1.4 \cdot 10^{-4} a32=0.66844129±1.5104a_{32}= -0.66844129 \pm 1.5 \cdot 10^{-4} a33=0.87439975±1.0104a_{33}= -0.87439975 \pm 1.0 \cdot 10^{-4}
a34=+0.08019490±1.4104a_{34}= +0.08019490 \pm 1.4 \cdot 10^{-4} a35=0.35212448±1.0104a_{35}= -0.35212448 \pm 1.0 \cdot 10^{-4} a36=+0.19314186±1.3104a_{36}= +0.19314186 \pm 1.3 \cdot 10^{-4}
a37=+0.14023588±1.6104a_{37}= +0.14023588 \pm 1.6 \cdot 10^{-4} a38=0.79129544±1.0104a_{38}= -0.79129544 \pm 1.0 \cdot 10^{-4} a39=+0.18670502±1.4104a_{39}= +0.18670502 \pm 1.4 \cdot 10^{-4}
a40=+0.30242142±1.1104a_{40}= +0.30242142 \pm 1.1 \cdot 10^{-4} a41=1.04120720±1.2104a_{41}= -1.04120720 \pm 1.2 \cdot 10^{-4} a42=+0.68603101±9.6105a_{42}= +0.68603101 \pm 9.6 \cdot 10^{-5}
a43=+1.13507617±1.3104a_{43}= +1.13507617 \pm 1.3 \cdot 10^{-4} a44=+0.45877696±1.2104a_{44}= +0.45877696 \pm 1.2 \cdot 10^{-4} a45=0.15195769±1.4104a_{45}= -0.15195769 \pm 1.4 \cdot 10^{-4}
a46=+0.48718103±1.4104a_{46}= +0.48718103 \pm 1.4 \cdot 10^{-4} a47=+1.29695332±1.3104a_{47}= +1.29695332 \pm 1.3 \cdot 10^{-4} a48=0.35143195±1.3104a_{48}= -0.35143195 \pm 1.3 \cdot 10^{-4}
a49=+0.60568875±1.2104a_{49}= +0.60568875 \pm 1.2 \cdot 10^{-4} a50=+0.74213595±1.2104a_{50}= +0.74213595 \pm 1.2 \cdot 10^{-4} a51=0.06712573±1.5104a_{51}= -0.06712573 \pm 1.5 \cdot 10^{-4}
a52=0.09795973±1.3104a_{52}= -0.09795973 \pm 1.3 \cdot 10^{-4} a53=+0.92117423±1.0104a_{53}= +0.92117423 \pm 1.0 \cdot 10^{-4} a54=+0.83744705±1.3104a_{54}= +0.83744705 \pm 1.3 \cdot 10^{-4}
a55=0.36095070±8.9105a_{55}= -0.36095070 \pm 8.9 \cdot 10^{-5} a56=1.37904264±1.0104a_{56}= -1.37904264 \pm 1.0 \cdot 10^{-4} a57=+0.66233991±1.0104a_{57}= +0.66233991 \pm 1.0 \cdot 10^{-4}
a58=0.64463075±9.8105a_{58}= -0.64463075 \pm 9.8 \cdot 10^{-5} a59=+1.84432955±1.2104a_{59}= +1.84432955 \pm 1.2 \cdot 10^{-4} a60=0.06607124±1.5104a_{60}= -0.06607124 \pm 1.5 \cdot 10^{-4}

Displaying ana_n with nn up to: 60 180 1000