Properties

Level $52$
Weight $0$
Character 52.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 52 = 2^{2} \cdot 13 \)
Weight: \( 0 \)
Character: 52.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.04687614337 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.439744072\) \(a_{4}=+0.000000000\) \(a_{5}=+0.789995633\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.624551231\) \(a_{8}=+0.000000000\) \(a_{9}=+1.072862994\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.848309637\) \(a_{12}=+0.000000000\) \(a_{13}=+0.277350098\) \(a_{14}=+0.000000000\) \(a_{15}=+1.137391530\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.820054742\) \(a_{18}=+0.000000000\) \(a_{19}=-0.663729756\) \(a_{20}=+0.000000000\)
\(a_{21}=+2.338938005\) \(a_{22}=+0.000000000\) \(a_{23}=+0.612769104\) \(a_{24}=+0.000000000\) \(a_{25}=-0.375906900\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.104904064\) \(a_{28}=+0.000000000\) \(a_{29}=-1.426918949\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.876670049\) \(a_{32}=+0.000000000\) \(a_{33}=-2.661092844\) \(a_{34}=+0.000000000\) \(a_{35}=+1.283388378\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.443332714\) \(a_{38}=+0.000000000\) \(a_{39}=+0.399313160\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.093494521\) \(a_{42}=+0.000000000\) \(a_{43}=-0.815770674\) \(a_{44}=+0.000000000\) \(a_{45}=+0.847557080\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.640341985\) \(a_{48}=+0.000000000\) \(a_{49}=+1.639166701\) \(a_{50}=+0.000000000\)
\(a_{51}=+1.180668954\) \(a_{52}=+0.000000000\) \(a_{53}=-1.355158077\) \(a_{54}=+0.000000000\) \(a_{55}=-1.460156541\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.955600982\) \(a_{58}=+0.000000000\) \(a_{59}=+0.299690750\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.502275243\) \(a_{62}=+0.000000000\) \(a_{63}=+1.742920898\) \(a_{64}=+0.000000000\) \(a_{65}=+0.219105366\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.101177817\) \(a_{68}=+0.000000000\) \(a_{69}=+0.882230685\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.973449228\) \(a_{72}=+0.000000000\) \(a_{73}=+0.759759914\) \(a_{74}=+0.000000000\) \(a_{75}=-0.541209731\)
\(a_{76}=+0.000000000\) \(a_{77}=-3.002673695\) \(a_{78}=+0.000000000\) \(a_{79}=-0.719134947\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.921827990\) \(a_{82}=+0.000000000\) \(a_{83}=+0.319656084\) \(a_{84}=+0.000000000\) \(a_{85}=+0.647839665\)
\(a_{86}=+0.000000000\) \(a_{87}=-2.054398098\) \(a_{88}=+0.000000000\) \(a_{89}=+0.091550301\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.450569443\) \(a_{92}=+0.000000000\) \(a_{93}=+1.262180506\) \(a_{94}=+0.000000000\) \(a_{95}=-0.524343609\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.805963983\) \(a_{98}=+0.000000000\) \(a_{99}=-1.982983011\) \(a_{100}=+0.000000000\)

Showing 100 of 456 available coefficients

Rows: Cols: