Properties

Label 15.41
Level 1515
Weight 00
Character 15.1
Symmetry even
RR 7.763330
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: even
Fricke sign: +1+1
Spectral parameter: 7.76333046177552089358528249615±210107.76333046177552089358528249615 \pm 2 \cdot 10^{-10}

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=+0.12760350±1108a_{2}= +0.12760350 \pm 1 \cdot 10^{-8} a3=0.57735027±1.0108a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.98371735±1108a_{4}= -0.98371735 \pm 1 \cdot 10^{-8} a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=0.07367192±1.2108a_{6}= -0.07367192 \pm 1.2 \cdot 10^{-8}
a7=1.05886184±1108a_{7}= -1.05886184 \pm 1 \cdot 10^{-8} a8=0.25312929±1108a_{8}= -0.25312929 \pm 1 \cdot 10^{-8} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=0.05706602±1.2108a_{10}= -0.05706602 \pm 1.2 \cdot 10^{-8} a11=1.26499776±1108a_{11}= -1.26499776 \pm 1 \cdot 10^{-8} a12=+0.56794947±1.2108a_{12}= +0.56794947 \pm 1.2 \cdot 10^{-8}
a13=0.14321873±1108a_{13}= -0.14321873 \pm 1 \cdot 10^{-8} a14=0.13511448±1108a_{14}= -0.13511448 \pm 1 \cdot 10^{-8} a15=+0.25819889±1.0108a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8}
a16=+0.95141716±1108a_{16}= +0.95141716 \pm 1 \cdot 10^{-8} a17=+0.96939605±1108a_{17}= +0.96939605 \pm 1 \cdot 10^{-8} a18=+0.04253450±1.2108a_{18}= +0.04253450 \pm 1.2 \cdot 10^{-8}
a19=+0.71773154±1108a_{19}= +0.71773154 \pm 1 \cdot 10^{-8} a20=+0.43993177±1.2108a_{20}= +0.43993177 \pm 1.2 \cdot 10^{-8} a21=+0.61133417±1.1108a_{21}= +0.61133417 \pm 1.1 \cdot 10^{-8}
a22=0.16141815±1108a_{22}= -0.16141815 \pm 1 \cdot 10^{-8} a23=+0.14193257±1108a_{23}= +0.14193257 \pm 1 \cdot 10^{-8} a24=+0.14614426±1.2108a_{24}= +0.14614426 \pm 1.2 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=0.01827521±1108a_{26}= -0.01827521 \pm 1 \cdot 10^{-8} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+1.04162076±1108a_{28}= +1.04162076 \pm 1 \cdot 10^{-8} a29=1.32427348±1108a_{29}= -1.32427348 \pm 1 \cdot 10^{-8} a30=+0.03294708±1.2108a_{30}= +0.03294708 \pm 1.2 \cdot 10^{-8}
a31=+1.54651753±1108a_{31}= +1.54651753 \pm 1 \cdot 10^{-8} a32=+0.37453345±1108a_{32}= +0.37453345 \pm 1 \cdot 10^{-8} a33=+0.73034680±1.1108a_{33}= +0.73034680 \pm 1.1 \cdot 10^{-8}
a34=+0.12369833±1108a_{34}= +0.12369833 \pm 1 \cdot 10^{-8} a35=+0.47353741±1.1108a_{35}= +0.47353741 \pm 1.1 \cdot 10^{-8} a36=0.32790578±1.2108a_{36}= -0.32790578 \pm 1.2 \cdot 10^{-8}
a37=1.57439501±1108a_{37}= -1.57439501 \pm 1 \cdot 10^{-8} a38=+0.09158506±1108a_{38}= +0.09158506 \pm 1 \cdot 10^{-8} a39=+0.08268737±1.1108a_{39}= +0.08268737 \pm 1.1 \cdot 10^{-8}
a40=+0.11320286±1.2108a_{40}= +0.11320286 \pm 1.2 \cdot 10^{-8} a41=0.78000760±1108a_{41}= -0.78000760 \pm 1 \cdot 10^{-8} a42=+0.07800838±1.3108a_{42}= +0.07800838 \pm 1.3 \cdot 10^{-8}
a43=0.50701566±1108a_{43}= -0.50701566 \pm 1 \cdot 10^{-8} a44=+1.24440024±1108a_{44}= +1.24440024 \pm 1 \cdot 10^{-8} a45=0.14907120±1.4107a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7}
a46=+0.01811109±1108a_{46}= +0.01811109 \pm 1 \cdot 10^{-8} a47=+0.55577976±1108a_{47}= +0.55577976 \pm 1 \cdot 10^{-8} a48=0.54930095±1.2108a_{48}= -0.54930095 \pm 1.2 \cdot 10^{-8}
a49=+0.12118839±1108a_{49}= +0.12118839 \pm 1 \cdot 10^{-8} a50=+0.02552070±1.2108a_{50}= +0.02552070 \pm 1.2 \cdot 10^{-8} a51=0.55968107±1.1108a_{51}= -0.55968107 \pm 1.1 \cdot 10^{-8}
a52=+0.14088675±1108a_{52}= +0.14088675 \pm 1 \cdot 10^{-8} a53=+0.85134830±1108a_{53}= +0.85134830 \pm 1 \cdot 10^{-8} a54=0.02455731±1.2108a_{54}= -0.02455731 \pm 1.2 \cdot 10^{-8}
a55=+0.56572420±1.1108a_{55}= +0.56572420 \pm 1.1 \cdot 10^{-8} a56=+0.26802894±1108a_{56}= +0.26802894 \pm 1 \cdot 10^{-8} a57=0.41438250±1.1108a_{57}= -0.41438250 \pm 1.1 \cdot 10^{-8}
a58=0.16898194±1108a_{58}= -0.16898194 \pm 1 \cdot 10^{-8} a59=+0.90190961±1108a_{59}= +0.90190961 \pm 1 \cdot 10^{-8} a60=0.25399473±1.2108a_{60}= -0.25399473 \pm 1.2 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000