Properties

Label 13.183
Level 1313
Weight 00
Character 13.1
Symmetry even
RR 14.39493
Fricke sign +1+1

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Maass form invariants

Level: 13 13
Weight: 0 0
Character: 13.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 14.3949315595531201586695527513±210714.3949315595531201586695527513 \pm 2 \cdot 10^{-7}

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=1.25797981±8.2106a_{2}= -1.25797981 \pm 8.2 \cdot 10^{-6} a3=+0.04706666±6.2106a_{3}= +0.04706666 \pm 6.2 \cdot 10^{-6}
a4=+0.58251320±8.8106a_{4}= +0.58251320 \pm 8.8 \cdot 10^{-6} a5=0.93246427±6.8106a_{5}= -0.93246427 \pm 6.8 \cdot 10^{-6} a6=0.05920891±7.9106a_{6}= -0.05920891 \pm 7.9 \cdot 10^{-6}
a7=+0.28929489±6.2106a_{7}= +0.28929489 \pm 6.2 \cdot 10^{-6} a8=+0.52518997±8.0106a_{8}= +0.52518997 \pm 8.0 \cdot 10^{-6} a9=0.99778473±5.5106a_{9}= -0.99778473 \pm 5.5 \cdot 10^{-6}
a10=+1.17302123±6.2106a_{10}= +1.17302123 \pm 6.2 \cdot 10^{-6} a11=0.96241305±4.6106a_{11}= -0.96241305 \pm 4.6 \cdot 10^{-6} a12=+0.02741695±7.8106a_{12}= +0.02741695 \pm 7.8 \cdot 10^{-6}
a13=0.27735010±1.0108a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} a14=0.36392712±8.8106a_{14}= -0.36392712 \pm 8.8 \cdot 10^{-6} a15=0.04388798±5.1106a_{15}= -0.04388798 \pm 5.1 \cdot 10^{-6}
a16=1.24319157±5.6106a_{16}= -1.24319157 \pm 5.6 \cdot 10^{-6} a17=+1.49466949±6.1106a_{17}= +1.49466949 \pm 6.1 \cdot 10^{-6} a18=+1.25519304±6.5106a_{18}= +1.25519304 \pm 6.5 \cdot 10^{-6}
a19=+0.37181090±6.6106a_{19}= +0.37181090 \pm 6.6 \cdot 10^{-6} a20=0.54317275±7.6106a_{20}= -0.54317275 \pm 7.6 \cdot 10^{-6} a21=+0.01361614±5.1106a_{21}= +0.01361614 \pm 5.1 \cdot 10^{-6}
a22=+1.21069618±4.4106a_{22}= +1.21069618 \pm 4.4 \cdot 10^{-6} a23=1.89419078±4.5106a_{23}= -1.89419078 \pm 4.5 \cdot 10^{-6} a24=+0.02471894±7.3106a_{24}= +0.02471894 \pm 7.3 \cdot 10^{-6}
a25=0.13051038±7.6106a_{25}= -0.13051038 \pm 7.6 \cdot 10^{-6} a26=+0.34890082±8.2106a_{26}= +0.34890082 \pm 8.2 \cdot 10^{-6} a27=0.09402906±6.7106a_{27}= -0.09402906 \pm 6.7 \cdot 10^{-6}
a28=+0.16851809±9.6106a_{28}= +0.16851809 \pm 9.6 \cdot 10^{-6} a29=1.79976694±5.9106a_{29}= -1.79976694 \pm 5.9 \cdot 10^{-6} a30=+0.05521019±4.2106a_{30}= +0.05521019 \pm 4.2 \cdot 10^{-6}
a31=0.29299591±4.6106a_{31}= -0.29299591 \pm 4.6 \cdot 10^{-6} a32=+1.03871993±6.1106a_{32}= +1.03871993 \pm 6.1 \cdot 10^{-6} a33=0.04529757±5.5106a_{33}= -0.04529757 \pm 5.5 \cdot 10^{-6}
a34=1.88026404±7.7106a_{34}= -1.88026404 \pm 7.7 \cdot 10^{-6} a35=0.26975715±5.6106a_{35}= -0.26975715 \pm 5.6 \cdot 10^{-6} a36=0.58122278±5.4106a_{36}= -0.58122278 \pm 5.4 \cdot 10^{-6}
a37=1.03786007±5.4106a_{37}= -1.03786007 \pm 5.4 \cdot 10^{-6} a38=0.46773060±8.8106a_{38}= -0.46773060 \pm 8.8 \cdot 10^{-6} a39=0.01305394±6.2106a_{39}= -0.01305394 \pm 6.2 \cdot 10^{-6}
a40=0.48972088±7.3106a_{40}= -0.48972088 \pm 7.3 \cdot 10^{-6} a41=0.11879255±9.1106a_{41}= -0.11879255 \pm 9.1 \cdot 10^{-6} a42=0.01712883±7.3106a_{42}= -0.01712883 \pm 7.3 \cdot 10^{-6}
a43=0.99232059±5.1106a_{43}= -0.99232059 \pm 5.1 \cdot 10^{-6} a44=0.56061831±3.6106a_{44}= -0.56061831 \pm 3.6 \cdot 10^{-6} a45=+0.93039861±4.7106a_{45}= +0.93039861 \pm 4.7 \cdot 10^{-6}
a46=+2.38285375±5.3106a_{46}= +2.38285375 \pm 5.3 \cdot 10^{-6} a47=1.40125276±4.7106a_{47}= -1.40125276 \pm 4.7 \cdot 10^{-6} a48=0.05851288±5.0106a_{48}= -0.05851288 \pm 5.0 \cdot 10^{-6}
a49=0.91630847±4.7106a_{49}= -0.91630847 \pm 4.7 \cdot 10^{-6} a50=+0.16417942±6.1106a_{50}= +0.16417942 \pm 6.1 \cdot 10^{-6} a51=+0.07034910±6.6106a_{51}= +0.07034910 \pm 6.6 \cdot 10^{-6}
a52=0.16156009±8.8106a_{52}= -0.16156009 \pm 8.8 \cdot 10^{-6} a53=+0.57104359±6.5106a_{53}= +0.57104359 \pm 6.5 \cdot 10^{-6} a54=+0.11828666±7.1106a_{54}= +0.11828666 \pm 7.1 \cdot 10^{-6}
a55=+0.89741579±4.4106a_{55}= +0.89741579 \pm 4.4 \cdot 10^{-6} a56=+0.15193477±7.5106a_{56}= +0.15193477 \pm 7.5 \cdot 10^{-6} a57=+0.01749990±3.7106a_{57}= +0.01749990 \pm 3.7 \cdot 10^{-6}
a58=+2.26407047±9.5106a_{58}= +2.26407047 \pm 9.5 \cdot 10^{-6} a59=+0.75117561±5.4106a_{59}= +0.75117561 \pm 5.4 \cdot 10^{-6} a60=0.02556533±4.9106a_{60}= -0.02556533 \pm 4.9 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000