Properties

Label 14.20
Level 1414
Weight 00
Character 14.1
Symmetry odd
RR 6.492565
Fricke sign 1-1

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Maass form invariants

Level: 14=27 14 = 2 \cdot 7
Weight: 0 0
Character: 14.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 6.4925656074380383424260045973±310116.4925656074380383424260045973 \pm 3 \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=+1.22382707±5.0108a_{3}= +1.22382707 \pm 5.0 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=0.28248102±3.8108a_{5}= -0.28248102 \pm 3.8 \cdot 10^{-8} a6=0.86537642±6.1108a_{6}= -0.86537642 \pm 6.1 \cdot 10^{-8}
a7=+0.37796447±1.0108a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} a8=0.35355339±4.2108a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} a9=+0.49775271±3.9108a_{9}= +0.49775271 \pm 3.9 \cdot 10^{-8}
a10=+0.19974425±4.9108a_{10}= +0.19974425 \pm 4.9 \cdot 10^{-8} a11=+0.89794832±3.9108a_{11}= +0.89794832 \pm 3.9 \cdot 10^{-8} a12=+0.61191354±6.1108a_{12}= +0.61191354 \pm 6.1 \cdot 10^{-8}
a13=+0.29003037±3.7108a_{13}= +0.29003037 \pm 3.7 \cdot 10^{-8} a14=0.26726124±1.0108a_{14}= -0.26726124 \pm 1.0 \cdot 10^{-8} a15=0.34570792±4.8108a_{15}= -0.34570792 \pm 4.8 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=+1.32917667±2.5108a_{17}= +1.32917667 \pm 2.5 \cdot 10^{-8} a18=0.35196431±5.0108a_{18}= -0.35196431 \pm 5.0 \cdot 10^{-8}
a19=+1.34350421±3.8108a_{19}= +1.34350421 \pm 3.8 \cdot 10^{-8} a20=0.14124051±4.9108a_{20}= -0.14124051 \pm 4.9 \cdot 10^{-8} a21=+0.46256315±6.1108a_{21}= +0.46256315 \pm 6.1 \cdot 10^{-8}
a22=0.63494535±5.0108a_{22}= -0.63494535 \pm 5.0 \cdot 10^{-8} a23=+0.60489660±3.5108a_{23}= +0.60489660 \pm 3.5 \cdot 10^{-8} a24=0.43268821±6.1108a_{24}= -0.43268821 \pm 6.1 \cdot 10^{-8}
a25=0.92020447±3.0108a_{25}= -0.92020447 \pm 3.0 \cdot 10^{-8} a26=0.20508244±4.7108a_{26}= -0.20508244 \pm 4.7 \cdot 10^{-8} a27=0.61466384±3.7108a_{27}= -0.61466384 \pm 3.7 \cdot 10^{-8}
a28=+0.18898224±9.4108a_{28}= +0.18898224 \pm 9.4 \cdot 10^{-8} a29=+1.51900790±4.3108a_{29}= +1.51900790 \pm 4.3 \cdot 10^{-8} a30=+0.24445242±9.9108a_{30}= +0.24445242 \pm 9.9 \cdot 10^{-8}
a31=0.56825713±4.2108a_{31}= -0.56825713 \pm 4.2 \cdot 10^{-8} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=+1.09893346±4.7108a_{33}= +1.09893346 \pm 4.7 \cdot 10^{-8}
a34=0.93986984±3.6108a_{34}= -0.93986984 \pm 3.6 \cdot 10^{-8} a35=0.10676779±4.9108a_{35}= -0.10676779 \pm 4.9 \cdot 10^{-8} a36=+0.24887635±5.0108a_{36}= +0.24887635 \pm 5.0 \cdot 10^{-8}
a37=+1.92710911±3.0108a_{37}= +1.92710911 \pm 3.0 \cdot 10^{-8} a38=0.95000094±4.9108a_{38}= -0.95000094 \pm 4.9 \cdot 10^{-8} a39=+0.35494702±4.3108a_{39}= +0.35494702 \pm 4.3 \cdot 10^{-8}
a40=+0.09987212±4.9108a_{40}= +0.09987212 \pm 4.9 \cdot 10^{-8} a41=0.59659368±2.5108a_{41}= -0.59659368 \pm 2.5 \cdot 10^{-8} a42=0.32708154±6.1108a_{42}= -0.32708154 \pm 6.1 \cdot 10^{-8}
a43=1.77495323±3.9108a_{43}= -1.77495323 \pm 3.9 \cdot 10^{-8} a44=+0.44897416±5.0108a_{44}= +0.44897416 \pm 5.0 \cdot 10^{-8} a45=0.14060569±3.4108a_{45}= -0.14060569 \pm 3.4 \cdot 10^{-8}
a46=0.42772649±4.5108a_{46}= -0.42772649 \pm 4.5 \cdot 10^{-8} a47=0.55854787±2.8108a_{47}= -0.55854787 \pm 2.8 \cdot 10^{-8} a48=+0.30595677±6.1108a_{48}= +0.30595677 \pm 6.1 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=+0.65068282±4.0108a_{50}= +0.65068282 \pm 4.0 \cdot 10^{-8} a51=+1.62668240±3.0108a_{51}= +1.62668240 \pm 3.0 \cdot 10^{-8}
a52=+0.14501519±4.7108a_{52}= +0.14501519 \pm 4.7 \cdot 10^{-8} a53=0.19240874±3.7108a_{53}= -0.19240874 \pm 3.7 \cdot 10^{-8} a54=+0.43463297±4.7108a_{54}= +0.43463297 \pm 4.7 \cdot 10^{-8}
a55=0.25365336±3.6108a_{55}= -0.25365336 \pm 3.6 \cdot 10^{-8} a56=0.13363062±1.6107a_{56}= -0.13363062 \pm 1.6 \cdot 10^{-7} a57=+1.64421682±5.4108a_{57}= +1.64421682 \pm 5.4 \cdot 10^{-8}
a58=1.07410078±5.3108a_{58}= -1.07410078 \pm 5.3 \cdot 10^{-8} a59=0.47432916±4.0108a_{59}= -0.47432916 \pm 4.0 \cdot 10^{-8} a60=0.17285396±9.9108a_{60}= -0.17285396 \pm 9.9 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000