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: \( 48.7416663476 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.010084864\) \(a_{3}=+0.695789203\) \(a_{4}=+0.020271433\) \(a_{5}=+0.859050047\)
\(a_{6}=-0.702806143\) \(a_{7}=+0.249816485\) \(a_{8}=+0.989608997\) \(a_{9}=-0.515877385\) \(a_{10}=-0.867713450\)
\(a_{11}=+1.095355146\) \(a_{12}=+0.014104644\) \(a_{13}=+0.630882555\) \(a_{14}=-0.252335850\) \(a_{15}=+0.597717748\)
\(a_{16}=-1.019860502\) \(a_{17}=+0.217883242\) \(a_{18}=+0.521079938\) \(a_{19}=+1.213792462\) \(a_{20}=+0.017414175\)
\(a_{21}=+0.173819613\) \(a_{22}=-1.106401655\) \(a_{23}=+1.785702277\) \(a_{24}=+0.688559255\) \(a_{25}=-0.262033016\)
\(a_{26}=-0.637244920\) \(a_{27}=-1.054731118\) \(a_{28}=+0.005064138\) \(a_{29}=-1.045768171\) \(a_{30}=-0.603745650\)
\(a_{31}=-1.626239679\) \(a_{32}=+0.040536660\) \(a_{33}=+0.762136284\) \(a_{34}=-0.220080565\) \(a_{35}=+0.214604863\)
\(a_{36}=-0.010457574\) \(a_{37}=-0.684893666\) \(a_{38}=-1.226033394\) \(a_{39}=+0.438961270\) \(a_{40}=+0.850123655\)
\(a_{41}=+0.339714851\) \(a_{42}=-0.175572560\) \(a_{43}=+1.250356190\) \(a_{44}=+0.022204418\) \(a_{45}=-0.443164492\)
\(a_{46}=-1.803710828\) \(a_{47}=+0.476439116\) \(a_{48}=-0.709607926\) \(a_{49}=-0.937591724\) \(a_{50}=+0.264675584\)
\(a_{51}=+0.151600807\) \(a_{52}=+0.012788893\) \(a_{53}=+1.151363604\) \(a_{54}=+1.065367938\) \(a_{55}=+0.940964890\)
\(a_{56}=+0.247220641\) \(a_{57}=+0.844543690\) \(a_{58}=+1.056314601\) \(a_{59}=+1.834821417\) \(a_{60}=+0.012116595\)
\(a_{61}=-0.827122949\) \(a_{62}=+1.642640085\) \(a_{63}=-0.128874675\) \(a_{64}=+0.978915036\) \(a_{65}=+0.541959689\)
\(a_{66}=-0.769822325\) \(a_{67}=-0.126882369\) \(a_{68}=+0.004416803\) \(a_{69}=+1.242472356\) \(a_{70}=-0.216769130\)
\(a_{71}=+0.024563420\) \(a_{72}=-0.510516901\) \(a_{73}=-0.232644226\) \(a_{74}=+0.691800725\) \(a_{75}=-0.182319744\)
\(a_{76}=+0.024605312\) \(a_{77}=+0.273637772\) \(a_{78}=-0.443388135\) \(a_{79}=+0.807082446\) \(a_{80}=-0.876111212\)
\(a_{81}=-0.217993139\) \(a_{82}=-0.343140829\) \(a_{83}=+1.450337464\) \(a_{84}=+0.003523573\) \(a_{85}=+0.187172609\)
\(a_{86}=-1.262965863\) \(a_{87}=-0.727634202\) \(a_{88}=+1.083973307\) \(a_{89}=+0.070964427\) \(a_{90}=+0.447633746\)
\(a_{91}=+0.157604862\) \(a_{92}=+0.036198743\) \(a_{93}=-1.131520010\) \(a_{94}=-0.481243940\) \(a_{95}=+1.042708472\)
\(a_{96}=+0.028204970\) \(a_{97}=-0.266666965\) \(a_{98}=+0.947047209\) \(a_{99}=-0.565068948\) \(a_{100}=-0.005311785\)

Showing 100 of 5000 available coefficients

Rows: Cols: