Properties

Level $4$
Weight $0$
Character 4.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 4 = 2^{2} \)
Weight: \( 0 \)
Character: 4.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.70330780122 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.538446770\) \(a_{4}=+0.000000000\) \(a_{5}=-0.599423786\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.880371342\) \(a_{8}=+0.000000000\) \(a_{9}=-0.710075076\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.209875599\) \(a_{12}=+0.000000000\) \(a_{13}=+1.016564352\) \(a_{14}=+0.000000000\) \(a_{15}=-0.322757801\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.094555170\) \(a_{18}=+0.000000000\) \(a_{19}=+0.808725878\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.474033105\) \(a_{22}=+0.000000000\) \(a_{23}=+0.021792091\) \(a_{24}=+0.000000000\) \(a_{25}=-0.640691124\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.920784401\) \(a_{28}=+0.000000000\) \(a_{29}=+1.219277102\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.522398952\) \(a_{32}=+0.000000000\) \(a_{33}=-0.113006839\) \(a_{34}=+0.000000000\) \(a_{35}=-0.527715523\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.860721221\) \(a_{38}=+0.000000000\) \(a_{39}=+0.547365795\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.204686380\) \(a_{42}=+0.000000000\) \(a_{43}=+1.294360490\) \(a_{44}=+0.000000000\) \(a_{45}=+0.425635890\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.407032266\) \(a_{48}=+0.000000000\) \(a_{49}=-0.224946333\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.589359675\) \(a_{52}=+0.000000000\) \(a_{53}=+0.813663196\) \(a_{54}=+0.000000000\) \(a_{55}=+0.125803449\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.435457933\) \(a_{58}=+0.000000000\) \(a_{59}=+0.837734647\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.778346069\) \(a_{62}=+0.000000000\) \(a_{63}=-0.625129748\) \(a_{64}=+0.000000000\) \(a_{65}=-0.609352856\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.102445426\) \(a_{68}=+0.000000000\) \(a_{69}=+0.011733882\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.594131168\) \(a_{72}=+0.000000000\) \(a_{73}=+0.220023712\) \(a_{74}=+0.000000000\) \(a_{75}=-0.344978070\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.184768474\) \(a_{78}=+0.000000000\) \(a_{79}=-0.320992720\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.214281694\) \(a_{82}=+0.000000000\) \(a_{83}=-1.881402123\) \(a_{84}=+0.000000000\) \(a_{85}=+0.656101862\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.656515836\) \(a_{88}=+0.000000000\) \(a_{89}=+0.353484433\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.894957197\) \(a_{92}=+0.000000000\) \(a_{93}=+0.281281836\) \(a_{94}=+0.000000000\) \(a_{95}=-0.484757843\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.992895153\) \(a_{98}=+0.000000000\) \(a_{99}=+0.149027440\) \(a_{100}=+0.000000000\)

Showing 100 of 5000 available coefficients

Rows: Cols: