Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 47.4228958985 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.615211590\) \(a_{3}=+0.343816815\) \(a_{4}=+1.608908480\) \(a_{5}=-0.314576386\)
\(a_{6}=-0.555336905\) \(a_{7}=-1.163989679\) \(a_{8}=-0.983516034\) \(a_{9}=-0.881789998\) \(a_{10}=+0.508107424\)
\(a_{11}=-1.767442744\) \(a_{12}=+0.553169789\) \(a_{13}=+0.916375619\) \(a_{14}=+1.880089620\) \(a_{15}=-0.108156651\)
\(a_{16}=-0.020321983\) \(a_{17}=+0.451637716\) \(a_{18}=+1.424277424\) \(a_{19}=-0.871949540\) \(a_{20}=-0.506124614\)
\(a_{21}=-0.400199225\) \(a_{22}=+2.854794010\) \(a_{23}=-0.334165323\) \(a_{24}=-0.338149350\) \(a_{25}=-0.901041698\)
\(a_{26}=-1.480140521\) \(a_{27}=-0.646991044\) \(a_{28}=-1.872752865\) \(a_{29}=-1.669940676\) \(a_{30}=+0.174695876\)
\(a_{31}=-0.445339522\) \(a_{32}=+1.016340337\) \(a_{33}=-0.607676535\) \(a_{34}=-0.729490474\) \(a_{35}=+0.366163666\)
\(a_{36}=-1.418719405\) \(a_{37}=+0.116629764\) \(a_{38}=+1.408383003\) \(a_{39}=+0.315065347\) \(a_{40}=+0.309390919\)
\(a_{41}=-0.381949900\) \(a_{42}=+0.646406425\) \(a_{43}=-0.013011465\) \(a_{44}=-2.843653619\) \(a_{45}=+0.277390310\)
\(a_{46}=+0.539747606\) \(a_{47}=-1.032631626\) \(a_{48}=-0.006987040\) \(a_{49}=+0.354871973\) \(a_{50}=+1.455372993\)
\(a_{51}=+0.155280641\) \(a_{52}=+1.474364504\) \(a_{53}=+0.520019372\) \(a_{54}=+1.045027432\) \(a_{55}=+0.555995750\)
\(a_{56}=+1.144802513\) \(a_{57}=-0.299790914\) \(a_{58}=+2.697307535\) \(a_{59}=-1.447132548\) \(a_{60}=-0.174014153\)
\(a_{61}=+0.991359104\) \(a_{62}=+0.719317558\) \(a_{63}=+1.026394456\) \(a_{64}=-1.621282707\) \(a_{65}=-0.288270131\)
\(a_{66}=+0.981526182\) \(a_{67}=-0.047023591\) \(a_{68}=+0.726643747\) \(a_{69}=-0.114891634\) \(a_{70}=-0.591431784\)
\(a_{71}=-0.943417751\) \(a_{72}=+0.867254601\) \(a_{73}=+0.886202301\) \(a_{74}=-0.188381746\) \(a_{75}=-0.309793287\)
\(a_{76}=-1.402887009\) \(a_{77}=+2.057285113\) \(a_{78}=-0.508897200\) \(a_{79}=-0.835847431\) \(a_{80}=+0.006392816\)
\(a_{81}=+0.659343598\) \(a_{82}=+0.616929905\) \(a_{83}=-0.346964825\) \(a_{84}=-0.643883926\) \(a_{85}=-0.142074560\)
\(a_{86}=+0.021016269\) \(a_{87}=-0.574153685\) \(a_{88}=+1.738308278\) \(a_{89}=+0.255282275\) \(a_{90}=-0.448044044\)
\(a_{91}=-1.066651763\) \(a_{92}=-0.537641326\) \(a_{93}=-0.153115216\) \(a_{94}=+1.667918570\) \(a_{95}=+0.274294735\)
\(a_{96}=+0.349434898\) \(a_{97}=-1.507329309\) \(a_{98}=-0.573193324\) \(a_{99}=+1.558513333\) \(a_{100}=-1.449693628\)

Showing 100 of 5000 available coefficients

Rows: Cols: