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: \( 24.9526483936 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.919549486\) \(a_{3}=-0.577350269\) \(a_{4}=+2.684670230\) \(a_{5}=-1.021762650\)
\(a_{6}=-1.108252412\) \(a_{7}=-0.592592330\) \(a_{8}=+3.233807874\) \(a_{9}=+0.333333333\) \(a_{10}=-1.961323970\)
\(a_{11}=-0.491771256\) \(a_{12}=-1.549995080\) \(a_{13}=-0.503568097\) \(a_{14}=-1.137510303\) \(a_{15}=+0.589914941\)
\(a_{16}=+3.522784012\) \(a_{17}=-1.415164676\) \(a_{18}=+0.639849829\) \(a_{19}=-0.541894396\) \(a_{20}=-2.743095768\)
\(a_{21}=+0.342133341\) \(a_{22}=-0.943979262\) \(a_{23}=-0.645749532\) \(a_{24}=-1.867039846\) \(a_{25}=+0.043998913\)
\(a_{26}=-0.966623882\) \(a_{27}=-0.192450090\) \(a_{28}=-1.590914988\) \(a_{29}=+0.247481468\) \(a_{30}=+1.132370922\)
\(a_{31}=-1.489593881\) \(a_{32}=+3.528350367\) \(a_{33}=+0.283924267\) \(a_{34}=-2.716478626\) \(a_{35}=+0.605488710\)
\(a_{36}=+0.894890076\) \(a_{37}=+1.073116517\) \(a_{38}=-1.040193109\) \(a_{39}=+0.290735176\) \(a_{40}=-3.304184102\)
\(a_{41}=-0.609266767\) \(a_{42}=+0.656741880\) \(a_{43}=+0.104991681\) \(a_{44}=-1.320243651\) \(a_{45}=-0.340587550\)
\(a_{46}=-1.239548182\) \(a_{47}=+1.076014204\) \(a_{48}=-2.033880297\) \(a_{49}=-0.648834330\) \(a_{50}=+0.084458091\)
\(a_{51}=+0.817045706\) \(a_{52}=-1.351914278\) \(a_{53}=+0.836024991\) \(a_{54}=-0.369417471\) \(a_{55}=+0.502473502\)
\(a_{56}=-1.916329744\) \(a_{57}=+0.312862875\) \(a_{58}=+0.475052925\) \(a_{59}=+0.078659401\) \(a_{60}=+1.583727080\)
\(a_{61}=-1.224139465\) \(a_{62}=-2.859349168\) \(a_{63}=-0.197530777\) \(a_{64}=+3.250059121\) \(a_{65}=+0.514527073\)
\(a_{66}=+0.545006681\) \(a_{67}=+0.345900831\) \(a_{68}=-3.799250475\) \(a_{69}=+0.372823666\) \(a_{70}=+1.162265542\)
\(a_{71}=-1.655446119\) \(a_{72}=+1.077935958\) \(a_{73}=-0.028431436\) \(a_{74}=+2.059900259\) \(a_{75}=-0.025402784\)
\(a_{76}=-1.454807752\) \(a_{77}=+0.291419875\) \(a_{78}=+0.558080558\) \(a_{79}=+1.318700517\) \(a_{80}=-3.599449128\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.169517710\) \(a_{83}=+1.581220482\) \(a_{84}=+0.918515196\) \(a_{85}=+1.445962409\)
\(a_{86}=+0.201536726\) \(a_{87}=-0.142883492\) \(a_{88}=-1.590293760\) \(a_{89}=+0.371745363\) \(a_{90}=-0.653774656\)
\(a_{91}=+0.298410592\) \(a_{92}=-1.733624544\) \(a_{93}=+0.860017428\) \(a_{94}=+2.065462513\) \(a_{95}=+0.553687454\)
\(a_{96}=-2.037094034\) \(a_{97}=+0.663726444\) \(a_{98}=-1.245469604\) \(a_{99}=-0.163923752\) \(a_{100}=+0.118122572\)

Showing 100 of 1228 available coefficients

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