Properties

Level $6$
Weight $0$
Character 6.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 16.3350572228 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.693219563\)
\(a_{6}=-0.408248290\) \(a_{7}=+1.450872207\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.490180254\)
\(a_{11}=+1.895477029\) \(a_{12}=+0.288675135\) \(a_{13}=+0.698938854\) \(a_{14}=-1.025921576\) \(a_{15}=+0.400230501\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.872022518\) \(a_{18}=-0.235702260\) \(a_{19}=-0.020074521\) \(a_{20}=+0.346609782\)
\(a_{21}=+0.837661459\) \(a_{22}=-1.340304661\) \(a_{23}=-1.275036427\) \(a_{24}=-0.204124145\) \(a_{25}=-0.519446637\)
\(a_{26}=-0.494224403\) \(a_{27}=+0.192450090\) \(a_{28}=+0.725436104\) \(a_{29}=+0.407970495\) \(a_{30}=-0.283005702\)
\(a_{31}=-0.143372887\) \(a_{32}=-0.176776695\) \(a_{33}=+1.094354173\) \(a_{34}=+0.616613036\) \(a_{35}=+1.005772998\)
\(a_{36}=+0.166666667\) \(a_{37}=+1.462205288\) \(a_{38}=+0.014194830\) \(a_{39}=+0.403532535\) \(a_{40}=-0.245090127\)
\(a_{41}=+1.350993919\) \(a_{42}=-0.592316098\) \(a_{43}=-0.601303729\) \(a_{44}=+0.947738515\) \(a_{45}=+0.231073188\)
\(a_{46}=+0.901586904\) \(a_{47}=-0.662027459\) \(a_{48}=+0.144337567\) \(a_{49}=+1.105030161\) \(a_{50}=+0.367304240\)
\(a_{51}=-0.503462436\) \(a_{52}=+0.349469427\) \(a_{53}=-1.260877220\) \(a_{54}=-0.136082763\) \(a_{55}=+1.313981758\)
\(a_{56}=-0.512960788\) \(a_{57}=-0.011590030\) \(a_{58}=-0.288478704\) \(a_{59}=-0.222059164\) \(a_{60}=+0.200115251\)
\(a_{61}=+0.280910740\) \(a_{62}=+0.101379941\) \(a_{63}=+0.483624069\) \(a_{64}=+0.125000000\) \(a_{65}=+0.484518087\)
\(a_{66}=-0.773825257\) \(a_{67}=+0.933526800\) \(a_{68}=-0.436011259\) \(a_{69}=-0.736142624\) \(a_{70}=-0.711188907\)
\(a_{71}=+0.822558999\) \(a_{72}=-0.117851130\) \(a_{73}=-0.586962000\) \(a_{74}=-1.033935275\) \(a_{75}=-0.299902656\)
\(a_{76}=-0.010037261\) \(a_{77}=+2.750094941\) \(a_{78}=-0.285340592\) \(a_{79}=+1.378180000\) \(a_{80}=+0.173304891\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.955296961\) \(a_{83}=-1.748330000\) \(a_{84}=+0.418830730\) \(a_{85}=-0.604503069\)
\(a_{86}=+0.425185944\) \(a_{87}=+0.235541875\) \(a_{88}=-0.670152331\) \(a_{89}=-0.038300000\) \(a_{90}=-0.163393418\)
\(a_{91}=+1.014070957\) \(a_{92}=-0.637518213\) \(a_{93}=-0.082776375\) \(a_{94}=+0.468124105\) \(a_{95}=-0.013916051\)
\(a_{96}=-0.102062073\) \(a_{97}=+1.670000000\) \(a_{98}=-0.781374320\) \(a_{99}=+0.631825676\) \(a_{100}=-0.259723319\)

Showing 100 of 102 available coefficients

Rows: Cols: