Properties

Label 11.133
Level 1111
Weight 00
Character 11.1
Symmetry odd
RR 13.54217
Fricke sign +1+1

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Maass form invariants

Level: 11 11
Weight: 0 0
Character: 11.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 13.5421737879709685184071760475±1010913.5421737879709685184071760475 \pm 10 \cdot 10^{-9}

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=+0.40646650±3.3105a_{2}= +0.40646650 \pm 3.3 \cdot 10^{-5} a3=1.84127746±2.7105a_{3}= -1.84127746 \pm 2.7 \cdot 10^{-5}
a4=0.83478498±3.9105a_{4}= -0.83478498 \pm 3.9 \cdot 10^{-5} a5=1.48852194±2.8105a_{5}= -1.48852194 \pm 2.8 \cdot 10^{-5} a6=0.74841761±3.4105a_{6}= -0.74841761 \pm 3.4 \cdot 10^{-5}
a7=+0.80165017±2.8105a_{7}= +0.80165017 \pm 2.8 \cdot 10^{-5} a8=0.74577863±3.3105a_{8}= -0.74577863 \pm 3.3 \cdot 10^{-5} a9=+2.39030267±3.1105a_{9}= +2.39030267 \pm 3.1 \cdot 10^{-5}
a10=0.60503431±3.5105a_{10}= -0.60503431 \pm 3.5 \cdot 10^{-5} a11=0.30151134±1.0108a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} a12=+1.53707077±3.6105a_{12}= +1.53707077 \pm 3.6 \cdot 10^{-5}
a13=+1.03237429±2.2105a_{13}= +1.03237429 \pm 2.2 \cdot 10^{-5} a14=+0.32584394±2.4105a_{14}= +0.32584394 \pm 2.4 \cdot 10^{-5} a15=+2.74078189±2.1105a_{15}= +2.74078189 \pm 2.1 \cdot 10^{-5}
a16=+0.53165095±2.9105a_{16}= +0.53165095 \pm 2.9 \cdot 10^{-5} a17=+0.00058707±2.8105a_{17}= +0.00058707 \pm 2.8 \cdot 10^{-5} a18=+0.97157797±3.1105a_{18}= +0.97157797 \pm 3.1 \cdot 10^{-5}
a19=1.06133060±2.0105a_{19}= -1.06133060 \pm 2.0 \cdot 10^{-5} a20=+1.24259576±3.8105a_{20}= +1.24259576 \pm 3.8 \cdot 10^{-5} a21=1.47606038±2.2105a_{21}= -1.47606038 \pm 2.2 \cdot 10^{-5}
a22=0.12255426±3.3105a_{22}= -0.12255426 \pm 3.3 \cdot 10^{-5} a23=0.97369245±2.6105a_{23}= -0.97369245 \pm 2.6 \cdot 10^{-5} a24=+1.37318539±3.8105a_{24}= +1.37318539 \pm 3.8 \cdot 10^{-5}
a25=+1.21569756±2.3105a_{25}= +1.21569756 \pm 2.3 \cdot 10^{-5} a26=+0.41962557±1.7105a_{26}= +0.41962557 \pm 1.7 \cdot 10^{-5} a27=2.55993296±2.6105a_{27}= -2.55993296 \pm 2.6 \cdot 10^{-5}
a28=0.66920552±2.9105a_{28}= -0.66920552 \pm 2.9 \cdot 10^{-5} a29=+0.92384540±2.6105a_{29}= +0.92384540 \pm 2.6 \cdot 10^{-5} a30=+1.11403603±2.0105a_{30}= +1.11403603 \pm 2.0 \cdot 10^{-5}
a31=+0.82574695±2.8105a_{31}= +0.82574695 \pm 2.8 \cdot 10^{-5} a32=+0.96187694±2.4105a_{32}= +0.96187694 \pm 2.4 \cdot 10^{-5} a33=+0.55516604±2.7105a_{33}= +0.55516604 \pm 2.7 \cdot 10^{-5}
a34=+0.00023862±3.4105a_{34}= +0.00023862 \pm 3.4 \cdot 10^{-5} a35=1.19327386±2.7105a_{35}= -1.19327386 \pm 2.7 \cdot 10^{-5} a36=1.99538877±3.2105a_{36}= -1.99538877 \pm 3.2 \cdot 10^{-5}
a37=+0.19738509±2.8105a_{37}= +0.19738509 \pm 2.8 \cdot 10^{-5} a38=0.43139534±2.8105a_{38}= -0.43139534 \pm 2.8 \cdot 10^{-5} a39=1.90088751±1.6105a_{39}= -1.90088751 \pm 1.6 \cdot 10^{-5}
a40=+1.11010786±2.7105a_{40}= +1.11010786 \pm 2.7 \cdot 10^{-5} a41=+0.69961162±1.8105a_{41}= +0.69961162 \pm 1.8 \cdot 10^{-5} a42=0.59996910±2.4105a_{42}= -0.59996910 \pm 2.4 \cdot 10^{-5}
a43=+0.66129722±2.7105a_{43}= +0.66129722 \pm 2.7 \cdot 10^{-5} a44=+0.25169714±3.9105a_{44}= +0.25169714 \pm 3.9 \cdot 10^{-5} a45=3.55801797±3.0105a_{45}= -3.55801797 \pm 3.0 \cdot 10^{-5}
a46=0.39577337±3.8105a_{46}= -0.39577337 \pm 3.8 \cdot 10^{-5} a47=+1.30289297±2.2105a_{47}= +1.30289297 \pm 2.2 \cdot 10^{-5} a48=0.97891691±3.0105a_{48}= -0.97891691 \pm 3.0 \cdot 10^{-5}
a49=0.35735701±2.5105a_{49}= -0.35735701 \pm 2.5 \cdot 10^{-5} a50=+0.49414034±3.6105a_{50}= +0.49414034 \pm 3.6 \cdot 10^{-5} a51=0.00108095±2.8105a_{51}= -0.00108095 \pm 2.8 \cdot 10^{-5}
a52=0.86181055±2.4105a_{52}= -0.86181055 \pm 2.4 \cdot 10^{-5} a53=1.20943553±2.2105a_{53}= -1.20943553 \pm 2.2 \cdot 10^{-5} a54=1.04052700±2.2105a_{54}= -1.04052700 \pm 2.2 \cdot 10^{-5}
a55=+0.44880625±2.8105a_{55}= +0.44880625 \pm 2.8 \cdot 10^{-5} a56=0.59785357±1.9105a_{56}= -0.59785357 \pm 1.9 \cdot 10^{-5} a57=+1.95420411±1.8105a_{57}= +1.95420411 \pm 1.8 \cdot 10^{-5}
a58=+0.37551221±2.5105a_{58}= +0.37551221 \pm 2.5 \cdot 10^{-5} a59=1.53744290±3.2105a_{59}= -1.53744290 \pm 3.2 \cdot 10^{-5} a60=2.28796356±1.7105a_{60}= -2.28796356 \pm 1.7 \cdot 10^{-5}

Displaying ana_n with nn up to: 60 180 1000