Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 21.8071264738 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.574385227\) \(a_{3}=-0.577350269\) \(a_{4}=-0.670081611\) \(a_{5}=-0.440215967\)
\(a_{6}=-0.331621466\) \(a_{7}=-0.256710756\) \(a_{8}=-0.959270206\) \(a_{9}=+0.333333333\) \(a_{10}=-0.252853548\)
\(a_{11}=-1.706000528\) \(a_{12}=+0.386871798\) \(a_{13}=-0.170877488\) \(a_{14}=-0.147450866\) \(a_{15}=+0.254158807\)
\(a_{16}=+0.119090975\) \(a_{17}=+0.166260929\) \(a_{18}=+0.191461742\) \(a_{19}=+1.465985737\) \(a_{20}=+0.294980624\)
\(a_{21}=+0.148212024\) \(a_{22}=-0.979901501\) \(a_{23}=-0.703558772\) \(a_{24}=+0.553834911\) \(a_{25}=-0.806209902\)
\(a_{26}=-0.098149505\) \(a_{27}=-0.192450090\) \(a_{28}=+0.172017157\) \(a_{29}=+1.153989150\) \(a_{30}=+0.145985064\)
\(a_{31}=+0.832053062\) \(a_{32}=+1.027674303\) \(a_{33}=+0.984959864\) \(a_{34}=+0.095497821\) \(a_{35}=+0.113008174\)
\(a_{36}=-0.223360537\) \(a_{37}=+1.609360625\) \(a_{38}=+0.842040551\) \(a_{39}=+0.098656163\) \(a_{40}=+0.422286061\)
\(a_{41}=-0.884673894\) \(a_{42}=+0.085130797\) \(a_{43}=-0.288167819\) \(a_{44}=+1.143159581\) \(a_{45}=-0.146738656\)
\(a_{46}=-0.404113765\) \(a_{47}=+1.511320843\) \(a_{48}=-0.068757207\) \(a_{49}=-0.934099588\) \(a_{50}=-0.463075058\)
\(a_{51}=-0.095990792\) \(a_{52}=+0.114501862\) \(a_{53}=+0.367210494\) \(a_{54}=-0.110540489\) \(a_{55}=+0.751008672\)
\(a_{56}=+0.246254980\) \(a_{57}=-0.846387260\) \(a_{58}=+0.662834320\) \(a_{59}=-0.312251001\) \(a_{60}=-0.170307143\)
\(a_{61}=-0.944205113\) \(a_{62}=+0.477918987\) \(a_{63}=-0.085570252\) \(a_{64}=+0.471189963\) \(a_{65}=+0.075222998\)
\(a_{66}=+0.565746395\) \(a_{67}=-0.557303213\) \(a_{68}=-0.111408391\) \(a_{69}=+0.406199846\) \(a_{70}=+0.064910226\)
\(a_{71}=+0.243196394\) \(a_{72}=-0.319756735\) \(a_{73}=-1.746987818\) \(a_{74}=+0.924392969\) \(a_{75}=+0.465465504\)
\(a_{76}=-0.982330084\) \(a_{77}=+0.437948686\) \(a_{78}=+0.056666643\) \(a_{79}=+1.803068670\) \(a_{80}=-0.052425749\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.508143616\) \(a_{83}=-1.363732670\) \(a_{84}=-0.099314152\) \(a_{85}=-0.073190716\)
\(a_{86}=-0.165519338\) \(a_{87}=-0.666255946\) \(a_{88}=+1.636515477\) \(a_{89}=+0.104137630\) \(a_{90}=-0.084284516\)
\(a_{91}=+0.043866089\) \(a_{92}=+0.471441795\) \(a_{93}=-0.480386059\) \(a_{94}=+0.868080366\) \(a_{95}=-0.645350329\)
\(a_{96}=-0.593328035\) \(a_{97}=+0.711248094\) \(a_{98}=-0.536533004\) \(a_{99}=-0.568666843\) \(a_{100}=+0.540226430\)

Showing 100 of 1228 available coefficients

Rows: Cols: