Properties

Level $2$
Weight $0$
Character 2.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 22.7582184887 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.695643493\) \(a_{4}=+0.500000000\) \(a_{5}=-0.255107963\)
\(a_{6}=+0.491894231\) \(a_{7}=-1.484079806\) \(a_{8}=+0.353553391\) \(a_{9}=-0.516080130\) \(a_{10}=-0.180388571\)
\(a_{11}=-0.772089403\) \(a_{12}=+0.347821747\) \(a_{13}=-0.907921094\) \(a_{14}=-1.049402894\) \(a_{15}=-0.177464195\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.010662088\) \(a_{18}=-0.364923760\) \(a_{19}=+0.945312660\) \(a_{20}=-0.127553982\)
\(a_{21}=-1.032390461\) \(a_{22}=-0.545949652\) \(a_{23}=-1.545227780\) \(a_{24}=+0.245947116\) \(a_{25}=-0.934919927\)
\(a_{26}=-0.641997163\) \(a_{27}=-1.054651278\) \(a_{28}=-0.742039903\) \(a_{29}=+1.267068487\) \(a_{30}=-0.125486136\)
\(a_{31}=-1.345071504\) \(a_{32}=+0.176776695\) \(a_{33}=-0.537098969\) \(a_{34}=+0.714646016\) \(a_{35}=+0.378600577\)
\(a_{36}=-0.258040065\) \(a_{37}=-0.687046003\) \(a_{38}=+0.668436992\) \(a_{39}=-0.631589402\) \(a_{40}=-0.090194285\)
\(a_{41}=+0.707903355\) \(a_{42}=-0.730010295\) \(a_{43}=+1.127795788\) \(a_{44}=-0.386044701\) \(a_{45}=+0.131656151\)
\(a_{46}=-1.092641041\) \(a_{47}=-0.046207583\) \(a_{48}=+0.173910873\) \(a_{49}=+1.202492870\) \(a_{50}=-0.661088220\)
\(a_{51}=+0.703060505\) \(a_{52}=-0.453960547\) \(a_{53}=-0.104286988\) \(a_{54}=-0.745751070\) \(a_{55}=+0.196966155\)
\(a_{56}=-0.524701447\) \(a_{57}=+0.657600601\) \(a_{58}=+0.895952719\) \(a_{59}=+0.387675023\) \(a_{60}=-0.088732097\)
\(a_{61}=-1.094503104\) \(a_{62}=-0.951109181\) \(a_{63}=+0.765904099\) \(a_{64}=+0.125000000\) \(a_{65}=+0.231617901\)
\(a_{66}=-0.379786323\) \(a_{67}=+0.675813221\) \(a_{68}=+0.505331044\) \(a_{69}=-1.074927651\) \(a_{70}=+0.267711035\)
\(a_{71}=+0.471003921\) \(a_{72}=-0.182461880\) \(a_{73}=-0.312587412\) \(a_{74}=-0.485814888\) \(a_{75}=-0.650370964\)
\(a_{76}=+0.472656330\) \(a_{77}=+1.145842291\) \(a_{78}=-0.446601149\) \(a_{79}=+0.741093250\) \(a_{80}=-0.063776991\)
\(a_{81}=-0.217581169\) \(a_{82}=+0.500563262\) \(a_{83}=-1.527532937\) \(a_{84}=-0.516195230\) \(a_{85}=-0.257827947\)
\(a_{86}=+0.797472049\) \(a_{87}=+0.881427948\) \(a_{88}=-0.272974826\) \(a_{89}=+0.003744179\) \(a_{90}=+0.093094957\)
\(a_{91}=+1.347427361\) \(a_{92}=-0.772613890\) \(a_{93}=-0.935690240\) \(a_{94}=-0.032673695\) \(a_{95}=-0.241156787\)
\(a_{96}=+0.122973558\) \(a_{97}=-0.958089066\) \(a_{98}=+0.850290863\) \(a_{99}=+0.398459999\) \(a_{100}=-0.467459963\)

Showing 100 of 1228 available coefficients

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