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: \( 6.69049934024 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.571268270\) \(a_{3}=-0.930967802\) \(a_{4}=+1.468883976\) \(a_{5}=-0.582522069\)
\(a_{6}=-1.462800168\) \(a_{7}=-0.541446884\) \(a_{8}=+0.736742514\) \(a_{9}=-0.133298951\) \(a_{10}=-0.915298444\)
\(a_{11}=-1.438238241\) \(a_{12}=-1.367483687\) \(a_{13}=+0.277350098\) \(a_{14}=-0.850758309\) \(a_{15}=+0.542309290\)
\(a_{16}=-0.311263840\) \(a_{17}=-0.306711438\) \(a_{18}=-0.209448412\) \(a_{19}=+1.051652715\) \(a_{20}=-0.855657333\)
\(a_{21}=+0.504069616\) \(a_{22}=-2.259858113\) \(a_{23}=+1.144939811\) \(a_{24}=-0.685883559\) \(a_{25}=-0.660668039\)
\(a_{26}=+0.435791409\) \(a_{27}=+1.055064834\) \(a_{28}=-0.795322653\) \(a_{29}=+1.269921275\) \(a_{30}=+0.852113381\)
\(a_{31}=-1.597810952\) \(a_{32}=-1.225821510\) \(a_{33}=+1.338953494\) \(a_{34}=-0.481925950\) \(a_{35}=+0.315404760\)
\(a_{36}=-0.195800693\) \(a_{37}=+0.067841834\) \(a_{38}=+1.652428542\) \(a_{39}=-0.258204010\) \(a_{40}=-0.429168774\)
\(a_{41}=-1.570351825\) \(a_{42}=+0.792028595\) \(a_{43}=+0.129510753\) \(a_{44}=-2.112605107\) \(a_{45}=+0.077649576\)
\(a_{46}=+1.799007595\) \(a_{47}=-0.139569374\) \(a_{48}=+0.289776594\) \(a_{49}=-0.706835300\) \(a_{50}=-1.038086668\)
\(a_{51}=+0.285538476\) \(a_{52}=+0.407395066\) \(a_{53}=+0.491513017\) \(a_{54}=+1.657790057\) \(a_{55}=+0.837805516\)
\(a_{56}=-0.398906939\) \(a_{57}=-0.979054817\) \(a_{58}=+1.995387004\) \(a_{59}=-0.719880153\) \(a_{60}=+0.796589427\)
\(a_{61}=-0.954818010\) \(a_{62}=-2.510589651\) \(a_{63}=+0.072174302\) \(a_{64}=-1.614830603\) \(a_{65}=-0.161562553\)
\(a_{66}=+2.103855141\) \(a_{67}=-1.148631553\) \(a_{68}=-0.450523517\) \(a_{69}=-1.065902099\) \(a_{70}=+0.495585490\)
\(a_{71}=+1.147120569\) \(a_{72}=-0.098207005\) \(a_{73}=+0.670955402\) \(a_{74}=+0.106597721\) \(a_{75}=+0.615060671\)
\(a_{76}=+1.544755823\) \(a_{77}=+0.778729614\) \(a_{78}=-0.405707771\) \(a_{79}=+1.899736685\) \(a_{80}=+0.181318053\)
\(a_{81}=-0.848932435\) \(a_{82}=-2.467443985\) \(a_{83}=-1.397522600\) \(a_{84}=+0.740419773\) \(a_{85}=+0.178666193\)
\(a_{86}=+0.203496143\) \(a_{87}=-1.182255831\) \(a_{88}=-1.059611259\) \(a_{89}=-0.420654285\) \(a_{90}=+0.122008307\)
\(a_{91}=-0.150170351\) \(a_{92}=+1.681783787\) \(a_{93}=+1.487510495\) \(a_{94}=-0.219300962\) \(a_{95}=-0.612610915\)
\(a_{96}=+1.141200358\) \(a_{97}=+0.376312716\) \(a_{98}=-1.110627834\) \(a_{99}=+0.191715649\) \(a_{100}=-0.970444696\)

Showing 100 of 1000 available coefficients

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