Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.53641204627 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.403793789\) \(a_{3}=+1.326890647\) \(a_{4}=-0.836950576\) \(a_{5}=-0.968924736\)
\(a_{6}=+0.535790202\) \(a_{7}=+1.229968594\) \(a_{8}=-0.741749233\) \(a_{9}=+0.760638790\) \(a_{10}=-0.391245790\)
\(a_{11}=+0.663407682\) \(a_{12}=-1.110541892\) \(a_{13}=+0.277350098\) \(a_{14}=+0.496653679\) \(a_{15}=-1.285657170\)
\(a_{16}=+0.537436843\) \(a_{17}=-1.311400383\) \(a_{18}=+0.307141219\) \(a_{19}=+0.048455350\) \(a_{20}=+0.810942116\)
\(a_{21}=+1.632033824\) \(a_{22}=+0.267879902\) \(a_{23}=+0.217967464\) \(a_{24}=-0.984220120\) \(a_{25}=-0.061184856\)
\(a_{26}=+0.111992247\) \(a_{27}=-0.317606151\) \(a_{28}=-1.029422924\) \(a_{29}=-1.203564159\) \(a_{30}=-0.519140380\)
\(a_{31}=+1.422337619\) \(a_{32}=+0.958762892\) \(a_{33}=+0.880269449\) \(a_{34}=-0.529535330\) \(a_{35}=-1.191746996\)
\(a_{36}=-0.636617074\) \(a_{37}=+0.566382364\) \(a_{38}=+0.019565969\) \(a_{39}=+0.368013251\) \(a_{40}=+0.718699180\)
\(a_{41}=+0.053760714\) \(a_{42}=+0.659005121\) \(a_{43}=+0.495365292\) \(a_{44}=-0.555239442\) \(a_{45}=-0.737001739\)
\(a_{46}=+0.088013908\) \(a_{47}=-0.158409648\) \(a_{48}=+0.713119920\) \(a_{49}=+0.512822743\) \(a_{50}=-0.024706065\)
\(a_{51}=-1.740084904\) \(a_{52}=-0.232128324\) \(a_{53}=+0.520384207\) \(a_{54}=-0.128247391\) \(a_{55}=-0.642792114\)
\(a_{56}=-0.912328261\) \(a_{57}=+0.064294951\) \(a_{58}=-0.485991732\) \(a_{59}=-0.597701497\) \(a_{60}=+1.076031510\)
\(a_{61}=+1.259013087\) \(a_{62}=+0.574331096\) \(a_{63}=+0.935561824\) \(a_{64}=-0.150294342\) \(a_{65}=-0.268731371\)
\(a_{66}=+0.355447336\) \(a_{67}=-0.911505361\) \(a_{68}=+1.097577306\) \(a_{69}=+0.289218990\) \(a_{70}=-0.481220035\)
\(a_{71}=+0.887817260\) \(a_{72}=-0.564203239\) \(a_{73}=-1.621267284\) \(a_{74}=+0.228701681\) \(a_{75}=-0.081185613\)
\(a_{76}=-0.040554733\) \(a_{77}=+0.815970614\) \(a_{78}=+0.148601465\) \(a_{79}=+0.464495203\) \(a_{80}=-0.520735851\)
\(a_{81}=-1.182067421\) \(a_{82}=+0.021708242\) \(a_{83}=+0.215920615\) \(a_{84}=-1.365931650\) \(a_{85}=+1.270648271\)
\(a_{86}=+0.200025428\) \(a_{87}=-1.596998026\) \(a_{88}=-0.492082140\) \(a_{89}=-0.120813247\) \(a_{90}=-0.297596725\)
\(a_{91}=+0.341131910\) \(a_{92}=-0.182427995\) \(a_{93}=+1.887286484\) \(a_{94}=-0.063964832\) \(a_{95}=-0.046949587\)
\(a_{96}=+1.272173515\) \(a_{97}=+1.459920975\) \(a_{98}=+0.207074638\) \(a_{99}=+0.504613617\) \(a_{100}=+0.051208700\)

Showing 100 of 546 available coefficients

Rows: Cols: