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: \( 15.4566814415 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.656844797\)
\(a_{6}=-0.408248290\) \(a_{7}=-1.557164778\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+1.171566191\)
\(a_{11}=+0.153648107\) \(a_{12}=+0.288675135\) \(a_{13}=-0.967142227\) \(a_{14}=+1.101081774\) \(a_{15}=-0.956579789\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.301467931\) \(a_{18}=-0.235702260\) \(a_{19}=+0.352345383\) \(a_{20}=-0.828422398\)
\(a_{21}=-0.899029504\) \(a_{22}=-0.108645619\) \(a_{23}=-1.612772480\) \(a_{24}=-0.204124145\) \(a_{25}=+1.745134680\)
\(a_{26}=+0.683872827\) \(a_{27}=+0.192450090\) \(a_{28}=-0.778582389\) \(a_{29}=-0.056547512\) \(a_{30}=+0.676404056\)
\(a_{31}=+1.932196946\) \(a_{32}=-0.176776695\) \(a_{33}=+0.088708776\) \(a_{34}=+0.213170018\) \(a_{35}=+2.579980359\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.399828083\) \(a_{38}=-0.249145810\) \(a_{39}=-0.558379825\) \(a_{40}=+0.585783095\)
\(a_{41}=+0.076254342\) \(a_{42}=+0.635709858\) \(a_{43}=+0.637467485\) \(a_{44}=+0.076824054\) \(a_{45}=-0.552281599\)
\(a_{46}=+1.140402357\) \(a_{47}=-0.800244212\) \(a_{48}=+0.144337567\) \(a_{49}=+1.424762145\) \(a_{50}=-1.233996566\)
\(a_{51}=-0.174052591\) \(a_{52}=-0.483571114\) \(a_{53}=+0.260330544\) \(a_{54}=-0.136082763\) \(a_{55}=-0.254571067\)
\(a_{56}=+0.550540887\) \(a_{57}=+0.203426702\) \(a_{58}=+0.039985129\) \(a_{59}=+0.782193894\) \(a_{60}=-0.478289895\)
\(a_{61}=+0.927747180\) \(a_{62}=-1.366269563\) \(a_{63}=-0.519054926\) \(a_{64}=+0.125000000\) \(a_{65}=+1.602404567\)
\(a_{66}=-0.062726577\) \(a_{67}=-0.268789390\) \(a_{68}=-0.150733966\) \(a_{69}=-0.931134625\) \(a_{70}=-1.824321607\)
\(a_{71}=+0.449422200\) \(a_{72}=-0.117851130\) \(a_{73}=+1.605784997\) \(a_{74}=+0.282721149\) \(a_{75}=+1.007553977\)
\(a_{76}=+0.176172692\) \(a_{77}=-0.239255421\) \(a_{78}=+0.394834161\) \(a_{79}=-0.416090000\) \(a_{80}=-0.414211199\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.053919962\) \(a_{83}=-1.192400000\) \(a_{84}=-0.449514752\) \(a_{85}=+0.499485573\)
\(a_{86}=-0.450757581\) \(a_{87}=-0.032647721\) \(a_{88}=-0.054322809\) \(a_{89}=-0.151000023\) \(a_{90}=+0.390522064\)
\(a_{91}=+1.505999811\) \(a_{92}=-0.806386240\) \(a_{93}=+1.115554427\) \(a_{94}=+0.565858109\) \(a_{95}=-0.583781615\)
\(a_{96}=-0.102062073\) \(a_{97}=-0.050000191\) \(a_{98}=-1.007458974\) \(a_{99}=+0.051216036\) \(a_{100}=+0.872567340\)

Showing 100 of 106 available coefficients

Rows: Cols: