Properties

Level $13$
Weight $0$
Character 13.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 4.46679817957 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.048892032\) \(a_{3}=+1.847826696\) \(a_{4}=+0.100174494\) \(a_{5}=+0.051475838\)
\(a_{6}=+1.938170698\) \(a_{7}=-0.089071897\) \(a_{8}=-0.943819803\) \(a_{9}=+2.414463499\) \(a_{10}=+0.053992597\)
\(a_{11}=-1.404557314\) \(a_{12}=+0.185105105\) \(a_{13}=-0.277350098\) \(a_{14}=-0.093426803\) \(a_{15}=+0.095118428\)
\(a_{16}=-1.090139565\) \(a_{17}=+1.018431912\) \(a_{18}=+2.532511525\) \(a_{19}=-0.300453661\) \(a_{20}=+0.005156566\)
\(a_{21}=-0.164589429\) \(a_{22}=-1.473228975\) \(a_{23}=+0.551301787\) \(a_{24}=-1.744015428\) \(a_{25}=-0.997350238\)
\(a_{26}=-0.290910308\) \(a_{27}=+2.613683415\) \(a_{28}=-0.008922732\) \(a_{29}=+0.319143879\) \(a_{30}=+0.099768962\)
\(a_{31}=+0.917431044\) \(a_{32}=-0.199618900\) \(a_{33}=-2.595378501\) \(a_{34}=+1.068225117\) \(a_{35}=-0.004585051\)
\(a_{36}=+0.241867660\) \(a_{37}=+0.996392345\) \(a_{38}=-0.315143451\) \(a_{39}=-0.512494915\) \(a_{40}=-0.048583916\)
\(a_{41}=+0.461560180\) \(a_{42}=-0.172636540\) \(a_{43}=+0.671816944\) \(a_{44}=-0.140700819\) \(a_{45}=+0.124286533\)
\(a_{46}=+0.578256052\) \(a_{47}=-1.338573124\) \(a_{48}=-2.014388991\) \(a_{49}=-0.992066197\) \(a_{50}=-1.046112718\)
\(a_{51}=+1.881885675\) \(a_{52}=-0.027783406\) \(a_{53}=+0.714384960\) \(a_{54}=+2.741471707\) \(a_{55}=-0.072300765\)
\(a_{56}=+0.084067820\) \(a_{57}=-0.555186296\) \(a_{58}=+0.334747472\) \(a_{59}=-0.456269587\) \(a_{60}=+0.009528440\)
\(a_{61}=-0.508622605\) \(a_{62}=+0.962286112\) \(a_{63}=-0.215060844\) \(a_{64}=+0.880760891\) \(a_{65}=-0.014276829\)
\(a_{66}=-2.722271829\) \(a_{67}=+0.034285410\) \(a_{68}=+0.102020902\) \(a_{69}=+1.018710160\) \(a_{70}=-0.004809223\)
\(a_{71}=+0.274021927\) \(a_{72}=-2.278818464\) \(a_{73}=+0.566015665\) \(a_{74}=+1.045107991\) \(a_{75}=-1.842930395\)
\(a_{76}=-0.030097794\) \(a_{77}=+0.125106584\) \(a_{78}=-0.537551833\) \(a_{79}=+0.895651123\) \(a_{80}=-0.056115848\)
\(a_{81}=+2.415170490\) \(a_{82}=+0.484126795\) \(a_{83}=-1.739082388\) \(a_{84}=-0.016487663\) \(a_{85}=+0.052424636\)
\(a_{86}=+0.704663439\) \(a_{87}=+0.589722580\) \(a_{88}=+1.325649007\) \(a_{89}=-0.797244620\) \(a_{90}=+0.130363154\)
\(a_{91}=+0.024704099\) \(a_{92}=+0.055226378\) \(a_{93}=+1.695253575\) \(a_{94}=-1.404018683\) \(a_{95}=-0.015466104\)
\(a_{96}=-0.368861133\) \(a_{97}=-0.958670498\) \(a_{98}=-1.040570329\) \(a_{99}=-3.391252368\) \(a_{100}=-0.099909056\)

Showing 100 of 546 available coefficients

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