Properties

Label 13.154
Level 1313
Weight 00
Character 13.1
Symmetry even
RR 13.14458
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: 13.1445892937610080453709428861±310813.1445892937610080453709428861 \pm 3 \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=0.30285279±1.1106a_{2}= -0.30285279 \pm 1.1 \cdot 10^{-6} a3=+0.21575518±8.8107a_{3}= +0.21575518 \pm 8.8 \cdot 10^{-7}
a4=0.90828019±1.2106a_{4}= -0.90828019 \pm 1.2 \cdot 10^{-6} a5=1.02721771±9.7107a_{5}= -1.02721771 \pm 9.7 \cdot 10^{-7} a6=0.06534206±1.1106a_{6}= -0.06534206 \pm 1.1 \cdot 10^{-6}
a7=+1.43198668±8.8107a_{7}= +1.43198668 \pm 8.8 \cdot 10^{-7} a8=+0.57792798±1.1106a_{8}= +0.57792798 \pm 1.1 \cdot 10^{-6} a9=0.95344970±7.8107a_{9}= -0.95344970 \pm 7.8 \cdot 10^{-7}
a10=+0.31109575±8.8107a_{10}= +0.31109575 \pm 8.8 \cdot 10^{-7} a11=1.39422847±6.6107a_{11}= -1.39422847 \pm 6.6 \cdot 10^{-7} a12=0.19596616±1.1106a_{12}= -0.19596616 \pm 1.1 \cdot 10^{-6}
a13=0.27735010±1.0108a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} a14=0.43368116±1.2106a_{14}= -0.43368116 \pm 1.2 \cdot 10^{-6} a15=0.22162754±7.2107a_{15}= -0.22162754 \pm 7.2 \cdot 10^{-7}
a16=+0.73325309±7.9107a_{16}= +0.73325309 \pm 7.9 \cdot 10^{-7} a17=0.54669496±8.6107a_{17}= -0.54669496 \pm 8.6 \cdot 10^{-7} a18=+0.28875490±9.2107a_{18}= +0.28875490 \pm 9.2 \cdot 10^{-7}
a19=1.85071656±9.4107a_{19}= -1.85071656 \pm 9.4 \cdot 10^{-7} a20=+0.93300149±1.0106a_{20}= +0.93300149 \pm 1.0 \cdot 10^{-6} a21=+0.30895854±7.2107a_{21}= +0.30895854 \pm 7.2 \cdot 10^{-7}
a22=+0.42224598±6.3107a_{22}= +0.42224598 \pm 6.3 \cdot 10^{-7} a23=+0.22745624±6.3107a_{23}= +0.22745624 \pm 6.3 \cdot 10^{-7} a24=+0.12469096±1.0106a_{24}= +0.12469096 \pm 1.0 \cdot 10^{-6}
a25=+0.05517621±1.0106a_{25}= +0.05517621 \pm 1.0 \cdot 10^{-6} a26=+0.08399625±1.1106a_{26}= +0.08399625 \pm 1.1 \cdot 10^{-6} a27=0.42146689±9.5107a_{27}= -0.42146689 \pm 9.5 \cdot 10^{-7}
a28=1.30064513±1.3106a_{28}= -1.30064513 \pm 1.3 \cdot 10^{-6} a29=+0.32871316±8.3107a_{29}= +0.32871316 \pm 8.3 \cdot 10^{-7} a30=+0.06712052±6.0107a_{30}= +0.06712052 \pm 6.0 \cdot 10^{-7}
a31=0.70094149±6.5107a_{31}= -0.70094149 \pm 6.5 \cdot 10^{-7} a32=0.79999572±8.6107a_{32}= -0.79999572 \pm 8.6 \cdot 10^{-7} a33=0.30081202±7.7107a_{33}= -0.30081202 \pm 7.7 \cdot 10^{-7}
a34=+0.16556809±1.1106a_{34}= +0.16556809 \pm 1.1 \cdot 10^{-6} a35=1.47096207±8.0107a_{35}= -1.47096207 \pm 8.0 \cdot 10^{-7} a36=+0.86599947±7.7107a_{36}= +0.86599947 \pm 7.7 \cdot 10^{-7}
a37=+1.58937437±7.7107a_{37}= +1.58937437 \pm 7.7 \cdot 10^{-7} a38=+0.56049467±1.2106a_{38}= +0.56049467 \pm 1.2 \cdot 10^{-6} a39=0.05983972±8.9107a_{39}= -0.05983972 \pm 8.9 \cdot 10^{-7}
a40=0.59365785±1.0106a_{40}= -0.59365785 \pm 1.0 \cdot 10^{-6} a41=1.40541165±1.2106a_{41}= -1.40541165 \pm 1.2 \cdot 10^{-6} a42=0.09356896±1.0106a_{42}= -0.09356896 \pm 1.0 \cdot 10^{-6}
a43=+0.69052302±7.3107a_{43}= +0.69052302 \pm 7.3 \cdot 10^{-7} a44=+1.26635010±5.1107a_{44}= +1.26635010 \pm 5.1 \cdot 10^{-7} a45=+0.97940042±6.7107a_{45}= +0.97940042 \pm 6.7 \cdot 10^{-7}
a46=0.06888576±7.5107a_{46}= -0.06888576 \pm 7.5 \cdot 10^{-7} a47=+0.38806137±6.7107a_{47}= +0.38806137 \pm 6.7 \cdot 10^{-7} a48=+0.15820315±7.1107a_{48}= +0.15820315 \pm 7.1 \cdot 10^{-7}
a49=+1.05058585±6.7107a_{49}= +1.05058585 \pm 6.7 \cdot 10^{-7} a50=0.01671027±8.6107a_{50}= -0.01671027 \pm 8.6 \cdot 10^{-7} a51=0.11795227±9.4107a_{51}= -0.11795227 \pm 9.4 \cdot 10^{-7}
a52=+0.25191160±1.2106a_{52}= +0.25191160 \pm 1.2 \cdot 10^{-6} a53=+1.10079537±9.3107a_{53}= +1.10079537 \pm 9.3 \cdot 10^{-7} a54=+0.12764242±1.0106a_{54}= +0.12764242 \pm 1.0 \cdot 10^{-6}
a55=+1.43217617±6.2107a_{55}= +1.43217617 \pm 6.2 \cdot 10^{-7} a56=+0.82758517±1.0106a_{56}= +0.82758517 \pm 1.0 \cdot 10^{-6} a57=0.39930169±5.3107a_{57}= -0.39930169 \pm 5.3 \cdot 10^{-7}
a58=0.09955170±1.3106a_{58}= -0.09955170 \pm 1.3 \cdot 10^{-6} a59=0.65845074±7.7107a_{59}= -0.65845074 \pm 7.7 \cdot 10^{-7} a60=+0.20129991±7.0107a_{60}= +0.20129991 \pm 7.0 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000