Properties

Level $33$
Weight $0$
Character 33.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 1.55606576917 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.039387426\) \(a_{3}=-0.577350267\) \(a_{4}=+0.080326236\) \(a_{5}=-1.076560494\)
\(a_{6}=+0.600090611\) \(a_{7}=-0.066781830\) \(a_{8}=+0.955897346\) \(a_{9}=+0.333333326\) \(a_{10}=+1.118963455\)
\(a_{11}=-0.301511342\) \(a_{12}=-0.046376365\) \(a_{13}=-0.821529464\) \(a_{14}=+0.069412195\) \(a_{15}=+0.621552487\)
\(a_{16}=-1.073873923\) \(a_{17}=-1.836431967\) \(a_{18}=-0.346462475\) \(a_{19}=+1.377857990\) \(a_{20}=-0.086476065\)
\(a_{21}=+0.038556503\) \(a_{22}=+0.313387103\) \(a_{23}=-0.720378842\) \(a_{24}=-0.551887582\) \(a_{25}=+0.158982503\)
\(a_{26}=+0.853887379\) \(a_{27}=-0.192450086\) \(a_{28}=-0.005364325\) \(a_{29}=+1.785437553\) \(a_{30}=-0.646033860\)
\(a_{31}=-0.409166416\) \(a_{32}=+0.160273692\) \(a_{33}=+0.174077642\) \(a_{34}=+1.908764331\) \(a_{35}=+0.071894732\)
\(a_{36}=+0.026775427\) \(a_{37}=-0.100995020\) \(a_{38}=-1.432128329\) \(a_{39}=+0.474310255\) \(a_{40}=-1.029081259\)
\(a_{41}=-0.522585167\) \(a_{42}=-0.040075137\) \(a_{43}=-0.257429742\) \(a_{44}=-0.024219362\) \(a_{45}=-0.358853587\)
\(a_{46}=+0.748752829\) \(a_{47}=+0.039997725\) \(a_{48}=+0.620001300\) \(a_{49}=-0.995540173\) \(a_{50}=-0.165244457\)
\(a_{51}=+1.060264499\) \(a_{52}=-0.065990169\) \(a_{53}=+0.565117687\) \(a_{54}=+0.200030181\) \(a_{55}=+0.324595218\)
\(a_{56}=-0.063836653\) \(a_{57}=-0.795506569\) \(a_{58}=-1.855761356\) \(a_{59}=-1.037072833\) \(a_{60}=+0.049926927\)
\(a_{61}=-0.202391090\) \(a_{62}=+0.425282420\) \(a_{63}=-0.022260620\) \(a_{64}=+0.907287454\) \(a_{65}=+0.884426172\)
\(a_{66}=-0.180934155\) \(a_{67}=-0.391883215\) \(a_{68}=-0.147513592\) \(a_{69}=+0.415910879\) \(a_{70}=-0.074726323\)
\(a_{71}=+0.990872017\) \(a_{72}=+0.318632412\) \(a_{73}=-0.576145069\) \(a_{74}=+0.104972823\) \(a_{75}=-0.091788424\)
\(a_{76}=+0.110678083\) \(a_{77}=+0.020135526\) \(a_{78}=-0.492992152\) \(a_{79}=+0.470026192\) \(a_{80}=+1.156090283\)
\(a_{81}=+0.111111108\) \(a_{82}=+0.543168519\) \(a_{83}=+0.081345817\) \(a_{84}=+0.003097088\) \(a_{85}=+1.977030099\)
\(a_{86}=+0.267569167\) \(a_{87}=-1.030822860\) \(a_{88}=-0.288213886\) \(a_{89}=-1.568914581\) \(a_{90}=+0.372987838\)
\(a_{91}=+0.054863254\) \(a_{92}=-0.057865360\) \(a_{93}=+0.236232355\) \(a_{94}=-0.041573085\) \(a_{95}=-1.483347485\)
\(a_{96}=-0.092534131\) \(a_{97}=-1.696088702\) \(a_{98}=+1.034751982\) \(a_{99}=-0.100503790\) \(a_{100}=+0.012770444\)

Showing 100 of 2000 available coefficients

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