Properties

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

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 6.320651643 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.827132484\) \(a_{3}=-1.727852519\) \(a_{4}=+2.338413116\) \(a_{5}=+0.086424943\)
\(a_{6}=+3.157015467\) \(a_{7}=-0.521768687\) \(a_{8}=-2.445458081\) \(a_{9}=+1.985474329\) \(a_{10}=-0.157909821\)
\(a_{11}=+1.368051125\) \(a_{12}=-4.040432994\) \(a_{13}=-0.277350098\) \(a_{14}=+0.953340517\) \(a_{15}=-0.149329555\)
\(a_{16}=+2.129762784\) \(a_{17}=-0.237182510\) \(a_{18}=-3.627724643\) \(a_{19}=+0.011113065\) \(a_{20}=+0.202097220\)
\(a_{21}=+0.901539340\) \(a_{22}=-2.499610652\) \(a_{23}=+1.189248481\) \(a_{24}=+4.225390907\) \(a_{25}=-0.992530729\)
\(a_{26}=+0.506755374\) \(a_{27}=-1.702754302\) \(a_{28}=-1.220110741\) \(a_{29}=+0.708068717\) \(a_{30}=+0.272844882\)
\(a_{31}=-0.256368070\) \(a_{32}=-1.445900686\) \(a_{33}=-2.363790584\) \(a_{34}=+0.433363868\) \(a_{35}=-0.045093829\)
\(a_{36}=+4.642859212\) \(a_{37}=-0.077253183\) \(a_{38}=-0.020305043\) \(a_{39}=+0.479220067\) \(a_{40}=-0.211348574\)
\(a_{41}=-1.068900324\) \(a_{42}=-1.647231813\) \(a_{43}=+0.417457174\) \(a_{44}=+3.199068694\) \(a_{45}=+0.171594500\)
\(a_{46}=-2.172914535\) \(a_{47}=+0.610054660\) \(a_{48}=-3.679916015\) \(a_{49}=-0.727757483\) \(a_{50}=+1.813485223\)
\(a_{51}=+0.409816397\) \(a_{52}=-0.648559107\) \(a_{53}=-0.682499068\) \(a_{54}=+3.111157698\) \(a_{55}=+0.118233741\)
\(a_{56}=+1.275963452\) \(a_{57}=-0.019201737\) \(a_{58}=-1.293735354\) \(a_{59}=-0.875566409\) \(a_{60}=-0.349194191\)
\(a_{61}=-1.230551452\) \(a_{62}=+0.468418429\) \(a_{63}=-1.035958333\) \(a_{64}=+0.512089328\) \(a_{65}=-0.023969967\)
\(a_{66}=+4.318958562\) \(a_{67}=+0.784796881\) \(a_{68}=-0.554630692\) \(a_{69}=-2.054845986\) \(a_{70}=+0.082392402\)
\(a_{71}=+1.928757283\) \(a_{72}=-4.855394244\) \(a_{73}=+0.881039736\) \(a_{74}=+0.141151799\) \(a_{75}=+1.714946719\)
\(a_{76}=+0.025986937\) \(a_{77}=-0.713806231\) \(a_{78}=-0.875598559\) \(a_{79}=-1.538795162\) \(a_{80}=+0.184064644\)
\(a_{81}=+0.956633960\) \(a_{82}=+1.953022505\) \(a_{83}=-0.849899409\) \(a_{84}=+2.108171398\) \(a_{85}=-0.020498521\)
\(a_{86}=-0.762749551\) \(a_{87}=-1.223438238\) \(a_{88}=-3.345511808\) \(a_{89}=+0.737727668\) \(a_{90}=-0.313525896\)
\(a_{91}=+0.144712596\) \(a_{92}=+2.780954246\) \(a_{93}=+0.442966218\) \(a_{94}=-1.114650635\) \(a_{95}=+0.000960446\)
\(a_{96}=+2.498303145\) \(a_{97}=-1.188290081\) \(a_{98}=+1.329709253\) \(a_{99}=+2.716230389\) \(a_{100}=-2.320946870\)

Showing 100 of 1000 available coefficients

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