Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 9.74374939916 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.295505636\) \(a_{3}=-0.577350269\) \(a_{4}=-0.912676419\) \(a_{5}=+1.451392060\)
\(a_{6}=+0.170610259\) \(a_{7}=+0.939594386\) \(a_{8}=+0.565206660\) \(a_{9}=+0.333333341\) \(a_{10}=-0.428894567\)
\(a_{11}=+0.035852608\) \(a_{12}=+0.526933158\) \(a_{13}=+0.265179212\) \(a_{14}=-0.277677673\) \(a_{15}=-0.837841274\)
\(a_{16}=+0.745654665\) \(a_{17}=-0.202430301\) \(a_{18}=-0.098501879\) \(a_{19}=+1.542292554\) \(a_{20}=-1.324651308\)
\(a_{21}=-0.542475071\) \(a_{22}=-0.010594600\) \(a_{23}=+0.536745999\) \(a_{24}=-0.326322218\) \(a_{25}=+1.106538913\)
\(a_{26}=-0.078360707\) \(a_{27}=-0.192450090\) \(a_{28}=-0.857545639\) \(a_{29}=-0.472605955\) \(a_{30}=+0.247622374\)
\(a_{31}=+1.240744711\) \(a_{32}=-0.785551818\) \(a_{33}=-0.020699419\) \(a_{34}=+0.059819295\) \(a_{35}=+1.363719831\)
\(a_{36}=-0.304225473\) \(a_{37}=-1.301574524\) \(a_{38}=-0.455756143\) \(a_{39}=-0.153098858\) \(a_{40}=+0.820336462\)
\(a_{41}=+0.003144837\) \(a_{42}=+0.160304439\) \(a_{43}=+0.369215159\) \(a_{44}=-0.032721683\) \(a_{45}=+0.483797361\)
\(a_{46}=-0.158611463\) \(a_{47}=-0.627403289\) \(a_{48}=-0.430503929\) \(a_{49}=-0.117162383\) \(a_{50}=-0.326988433\)
\(a_{51}=+0.116873165\) \(a_{52}=-0.242019060\) \(a_{53}=+1.514320309\) \(a_{54}=+0.056870209\) \(a_{55}=+0.052036200\)
\(a_{56}=+0.531064545\) \(a_{57}=-0.890443321\) \(a_{58}=+0.139658007\) \(a_{59}=-1.459457313\) \(a_{60}=+0.764787939\)
\(a_{61}=+0.058387059\) \(a_{62}=-0.366647055\) \(a_{63}=+0.313198130\) \(a_{64}=-0.513519674\) \(a_{65}=+0.384872885\)
\(a_{66}=+0.006116794\) \(a_{67}=+1.206508344\) \(a_{68}=+0.184753368\) \(a_{69}=-0.309890447\) \(a_{70}=-0.402986905\)
\(a_{71}=-0.213301924\) \(a_{72}=+0.188402226\) \(a_{73}=-0.253254541\) \(a_{74}=+0.384622590\) \(a_{75}=-0.638860560\)
\(a_{76}=-1.407614039\) \(a_{77}=+0.033686794\) \(a_{78}=+0.045241606\) \(a_{79}=+1.572547912\) \(a_{80}=+1.082237232\)
\(a_{81}=+0.111111141\) \(a_{82}=-0.000929203\) \(a_{83}=-1.195638134\) \(a_{84}=+0.495104009\) \(a_{85}=-0.293805692\)
\(a_{86}=-0.109105064\) \(a_{87}=+0.272859445\) \(a_{88}=+0.020263732\) \(a_{89}=-1.001396546\) \(a_{90}=-0.142964621\)
\(a_{91}=+0.249157384\) \(a_{92}=-0.489874711\) \(a_{93}=-0.716345699\) \(a_{94}=+0.185400516\) \(a_{95}=+2.238471522\)
\(a_{96}=+0.453540690\) \(a_{97}=-0.104883977\) \(a_{98}=+0.034617478\) \(a_{99}=+0.011950244\) \(a_{100}=-1.009910677\)

Showing 100 of 5000 available coefficients

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