Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 30.5644447508 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.943302886\) \(a_{3}=+0.577350269\) \(a_{4}=-0.110179666\) \(a_{5}=+1.847801644\)
\(a_{6}=-0.544616175\) \(a_{7}=-0.919555161\) \(a_{8}=+1.047235682\) \(a_{9}=+0.333333333\) \(a_{10}=-1.743036623\)
\(a_{11}=-0.049458744\) \(a_{12}=-0.063612260\) \(a_{13}=+1.397662545\) \(a_{14}=+0.867419037\) \(a_{15}=+1.066828777\)
\(a_{16}=-0.877680775\) \(a_{17}=-0.028087965\) \(a_{18}=-0.314434295\) \(a_{19}=+1.398132168\) \(a_{20}=-0.203590168\)
\(a_{21}=-0.530905420\) \(a_{22}=+0.046654576\) \(a_{23}=+0.150994944\) \(a_{24}=+0.604621803\) \(a_{25}=+2.414370917\)
\(a_{26}=-1.318419112\) \(a_{27}=+0.192450090\) \(a_{28}=+0.101316281\) \(a_{29}=+0.057171027\) \(a_{30}=-1.006342664\)
\(a_{31}=-0.292597732\) \(a_{32}=-0.219316875\) \(a_{33}=-0.028555019\) \(a_{34}=+0.026495459\) \(a_{35}=-1.699155539\)
\(a_{36}=-0.036726555\) \(a_{37}=-1.326695867\) \(a_{38}=-1.318862109\) \(a_{39}=+0.806940846\) \(a_{40}=+1.935083816\)
\(a_{41}=-1.778225122\) \(a_{42}=+0.500804614\) \(a_{43}=+0.466371190\) \(a_{44}=+0.005449348\) \(a_{45}=+0.615933881\)
\(a_{46}=-0.142433967\) \(a_{47}=+0.440219423\) \(a_{48}=-0.506729232\) \(a_{49}=-0.154418306\) \(a_{50}=-2.277483053\)
\(a_{51}=-0.016216594\) \(a_{52}=-0.153993992\) \(a_{53}=+0.445541223\) \(a_{54}=-0.181538725\) \(a_{55}=-0.091389949\)
\(a_{56}=-0.962990977\) \(a_{57}=+0.807211984\) \(a_{58}=-0.053929595\) \(a_{59}=+1.055081146\) \(a_{60}=-0.117542838\)
\(a_{61}=+1.092059720\) \(a_{62}=+0.276008285\) \(a_{63}=-0.306518387\) \(a_{64}=+1.084563016\) \(a_{65}=+2.582603148\)
\(a_{66}=+0.026936032\) \(a_{67}=-0.143974249\) \(a_{68}=+0.003094723\) \(a_{69}=+0.087176972\) \(a_{70}=+1.602818323\)
\(a_{71}=-0.406643247\) \(a_{72}=+0.349078561\) \(a_{73}=+0.021760544\) \(a_{74}=+1.251476039\) \(a_{75}=+1.393937699\)
\(a_{76}=-0.154045735\) \(a_{77}=+0.045480044\) \(a_{78}=-0.761189629\) \(a_{79}=+0.365365732\) \(a_{80}=-1.621779980\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.677404889\) \(a_{83}=+0.871474382\) \(a_{84}=+0.058494982\) \(a_{85}=-0.051900988\)
\(a_{86}=-0.439929290\) \(a_{87}=+0.033007708\) \(a_{88}=-0.051794962\) \(a_{89}=+1.023735594\) \(a_{90}=-0.581012208\)
\(a_{91}=-1.285227806\) \(a_{92}=-0.016636573\) \(a_{93}=-0.168931379\) \(a_{94}=-0.415260252\) \(a_{95}=+2.583470919\)
\(a_{96}=-0.126622657\) \(a_{97}=-0.461546566\) \(a_{98}=+0.145663233\) \(a_{99}=-0.016486248\) \(a_{100}=-0.266014581\)

Showing 100 of 1228 available coefficients

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