Properties

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

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 20.6678761954 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.759837188\) \(a_{4}=+0.500000000\) \(a_{5}=+1.166130138\)
\(a_{6}=-0.537286028\) \(a_{7}=-0.912752281\) \(a_{8}=+0.353553391\) \(a_{9}=-0.422647448\) \(a_{10}=+0.824578529\)
\(a_{11}=+1.343335628\) \(a_{12}=-0.379918594\) \(a_{13}=+0.215244777\) \(a_{14}=-0.645413327\) \(a_{15}=-0.886069045\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.479738097\) \(a_{18}=-0.298856876\) \(a_{19}=+1.435008652\) \(a_{20}=+0.583065069\)
\(a_{21}=+0.693543126\) \(a_{22}=+0.949881732\) \(a_{23}=+0.213729803\) \(a_{24}=-0.268643014\) \(a_{25}=+0.359859500\)
\(a_{26}=+0.152201042\) \(a_{27}=+1.080980436\) \(a_{28}=-0.456376140\) \(a_{29}=-0.684782427\) \(a_{30}=-0.626545430\)
\(a_{31}=+1.597386166\) \(a_{32}=+0.176776695\) \(a_{33}=-1.020716366\) \(a_{34}=+1.046332843\) \(a_{35}=-1.064387943\)
\(a_{36}=-0.211323724\) \(a_{37}=+0.091626110\) \(a_{38}=+1.014704349\) \(a_{39}=-0.163550986\) \(a_{40}=+0.412289264\)
\(a_{41}=-1.367140882\) \(a_{42}=+0.490409048\) \(a_{43}=-0.342300947\) \(a_{44}=+0.671667814\) \(a_{45}=-0.492861927\)
\(a_{46}=+0.151129793\) \(a_{47}=+0.646152931\) \(a_{48}=-0.189959297\) \(a_{49}=-0.166883274\) \(a_{50}=+0.254459092\)
\(a_{51}=-1.124360035\) \(a_{52}=+0.107622389\) \(a_{53}=-0.312381111\) \(a_{54}=+0.764368597\) \(a_{55}=+1.566504161\)
\(a_{56}=-0.322706664\) \(a_{57}=-1.090372939\) \(a_{58}=-0.484214297\) \(a_{59}=+0.334175027\) \(a_{60}=-0.443034523\)
\(a_{61}=-0.491194033\) \(a_{62}=+1.129522590\) \(a_{63}=+0.385772422\) \(a_{64}=+0.125000000\) \(a_{65}=+0.251003422\)
\(a_{66}=-0.721755464\) \(a_{67}=-0.563071888\) \(a_{68}=+0.739869049\) \(a_{69}=-0.162399853\) \(a_{70}=-0.752635933\)
\(a_{71}=-0.033713976\) \(a_{72}=-0.149428438\) \(a_{73}=+1.329011679\) \(a_{74}=+0.064789444\) \(a_{75}=-0.273434630\)
\(a_{76}=+0.717504326\) \(a_{77}=-1.226132658\) \(a_{78}=-0.115648012\) \(a_{79}=+0.427324347\) \(a_{80}=+0.291532535\)
\(a_{81}=-0.398721687\) \(a_{82}=-0.966714588\) \(a_{83}=-0.263129154\) \(a_{84}=+0.346771563\) \(a_{85}=+1.725567192\)
\(a_{86}=-0.242043321\) \(a_{87}=+0.520323153\) \(a_{88}=+0.474940866\) \(a_{89}=-1.559592917\) \(a_{90}=-0.348506011\)
\(a_{91}=-0.196465161\) \(a_{92}=+0.106864902\) \(a_{93}=-1.213753412\) \(a_{94}=+0.456899119\) \(a_{95}=+1.673406838\)
\(a_{96}=-0.134321507\) \(a_{97}=+0.463854294\) \(a_{98}=-0.118004295\) \(a_{99}=-0.567757374\) \(a_{100}=+0.179929750\)

Showing 100 of 1228 available coefficients

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