Properties

Label 15.99
Level 1515
Weight 00
Character 15.1
Symmetry odd
RR 12.22540
Fricke sign +1+1

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Maass form invariants

Level: 15=35 15 = 3 \cdot 5
Weight: 0 0
Character: 15.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 12.2254089157236274658501505337±210812.2254089157236274658501505337 \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=+0.08727140±6.3105a_{2}= +0.08727140 \pm 6.3 \cdot 10^{-5} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.99238370±6.3105a_{4}= -0.99238370 \pm 6.3 \cdot 10^{-5} a5=+0.44721360±1.0108a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} a6=+0.05038616±6.3105a_{6}= +0.05038616 \pm 6.3 \cdot 10^{-5}
a7=0.44505338±5.4105a_{7}= -0.44505338 \pm 5.4 \cdot 10^{-5} a8=0.17387811±4.5105a_{8}= -0.17387811 \pm 4.5 \cdot 10^{-5} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=+0.03902895±6.3105a_{10}= +0.03902895 \pm 6.3 \cdot 10^{-5} a11=+0.71673436±5.5105a_{11}= +0.71673436 \pm 5.5 \cdot 10^{-5} a12=0.57295300±6.3105a_{12}= -0.57295300 \pm 6.3 \cdot 10^{-5}
a13=+0.24291178±5.4105a_{13}= +0.24291178 \pm 5.4 \cdot 10^{-5} a14=0.03884043±6.4105a_{14}= -0.03884043 \pm 6.4 \cdot 10^{-5} a15=+0.25819889±1.0108a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8}
a16=+0.97720912±5.3105a_{16}= +0.97720912 \pm 5.3 \cdot 10^{-5} a17=0.03834011±4.7105a_{17}= -0.03834011 \pm 4.7 \cdot 10^{-5} a18=+0.02909047±6.3105a_{18}= +0.02909047 \pm 6.3 \cdot 10^{-5}
a19=1.36361919±4.7105a_{19}= -1.36361919 \pm 4.7 \cdot 10^{-5} a20=0.44380748±6.3105a_{20}= -0.44380748 \pm 6.3 \cdot 10^{-5} a21=0.25695169±5.4105a_{21}= -0.25695169 \pm 5.4 \cdot 10^{-5}
a22=+0.06255041±6.5105a_{22}= +0.06255041 \pm 6.5 \cdot 10^{-5} a23=0.11093054±4.2105a_{23}= -0.11093054 \pm 4.2 \cdot 10^{-5} a24=0.10038857±4.5105a_{24}= -0.10038857 \pm 4.5 \cdot 10^{-5}
a25=+0.2a_{25}= +0.2 a26=+0.02119925±7.0105a_{26}= +0.02119925 \pm 7.0 \cdot 10^{-5} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+0.44166372±7.0105a_{28}= +0.44166372 \pm 7.0 \cdot 10^{-5} a29=0.55720135±3.5105a_{29}= -0.55720135 \pm 3.5 \cdot 10^{-5} a30=+0.02253338±6.3105a_{30}= +0.02253338 \pm 6.3 \cdot 10^{-5}
a31=+0.51708233±2.8105a_{31}= +0.51708233 \pm 2.8 \cdot 10^{-5} a32=+0.25916051±4.8105a_{32}= +0.25916051 \pm 4.8 \cdot 10^{-5} a33=+0.41380678±5.5105a_{33}= +0.41380678 \pm 5.5 \cdot 10^{-5}
a34=0.00334599±6.0105a_{34}= -0.00334599 \pm 6.0 \cdot 10^{-5} a35=0.19903392±5.4105a_{35}= -0.19903392 \pm 5.4 \cdot 10^{-5} a36=0.33079457±6.3105a_{36}= -0.33079457 \pm 6.3 \cdot 10^{-5}
a37=+1.36437633±4.1105a_{37}= +1.36437633 \pm 4.1 \cdot 10^{-5} a38=0.11900495±5.3105a_{38}= -0.11900495 \pm 5.3 \cdot 10^{-5} a39=+0.14024518±5.4105a_{39}= +0.14024518 \pm 5.4 \cdot 10^{-5}
a40=0.07776065±4.5105a_{40}= -0.07776065 \pm 4.5 \cdot 10^{-5} a41=1.42026118±4.8105a_{41}= -1.42026118 \pm 4.8 \cdot 10^{-5} a42=0.02242453±1.1104a_{42}= -0.02242453 \pm 1.1 \cdot 10^{-4}
a43=1.28002518±5.2105a_{43}= -1.28002518 \pm 5.2 \cdot 10^{-5} a44=0.71127550±5.1105a_{44}= -0.71127550 \pm 5.1 \cdot 10^{-5} a45=+0.14907120±1.4107a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7}
a46=0.00968106±3.1105a_{46}= -0.00968106 \pm 3.1 \cdot 10^{-5} a47=1.62606054±6.3105a_{47}= -1.62606054 \pm 6.3 \cdot 10^{-5} a48=+0.56419195±5.3105a_{48}= +0.56419195 \pm 5.3 \cdot 10^{-5}
a49=0.80192749±4.0105a_{49}= -0.80192749 \pm 4.0 \cdot 10^{-5} a50=+0.01745428±6.3105a_{50}= +0.01745428 \pm 6.3 \cdot 10^{-5} a51=0.02213567±4.8105a_{51}= -0.02213567 \pm 4.8 \cdot 10^{-5}
a52=0.24106169±5.6105a_{52}= -0.24106169 \pm 5.6 \cdot 10^{-5} a53=0.51990822±6.7105a_{53}= -0.51990822 \pm 6.7 \cdot 10^{-5} a54=+0.01679539±6.3105a_{54}= +0.01679539 \pm 6.3 \cdot 10^{-5}
a55=+0.32053335±5.5105a_{55}= +0.32053335 \pm 5.5 \cdot 10^{-5} a56=+0.07738504±4.6105a_{56}= +0.07738504 \pm 4.6 \cdot 10^{-5} a57=0.78728591±4.7105a_{57}= -0.78728591 \pm 4.7 \cdot 10^{-5}
a58=0.04862774±4.6105a_{58}= -0.04862774 \pm 4.6 \cdot 10^{-5} a59=1.10187802±4.4105a_{59}= -1.10187802 \pm 4.4 \cdot 10^{-5} a60=0.25623237±6.3105a_{60}= -0.25623237 \pm 6.3 \cdot 10^{-5}

Displaying ana_n with nn up to: 60 180 1000