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: \( 16.9653979482 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.271406213\) \(a_{3}=-0.577350269\) \(a_{4}=-0.926338668\) \(a_{5}=+0.887011418\)
\(a_{6}=+0.156696450\) \(a_{7}=+0.442334088\) \(a_{8}=+0.522820282\) \(a_{9}=+0.333333333\) \(a_{10}=-0.240740410\)
\(a_{11}=-0.482094189\) \(a_{12}=+0.534821879\) \(a_{13}=+1.366153977\) \(a_{14}=-0.120052220\) \(a_{15}=-0.512116281\)
\(a_{16}=+0.784441995\) \(a_{17}=-1.204068007\) \(a_{18}=-0.090468738\) \(a_{19}=-1.584901481\) \(a_{20}=-0.821672976\)
\(a_{21}=-0.255381705\) \(a_{22}=+0.130843358\) \(a_{23}=-0.889387416\) \(a_{24}=-0.301850431\) \(a_{25}=-0.213210744\)
\(a_{26}=-0.370782677\) \(a_{27}=-0.192450090\) \(a_{28}=-0.409751170\) \(a_{29}=+1.360677125\) \(a_{30}=+0.138991540\)
\(a_{31}=-1.055648525\) \(a_{32}=-0.735722713\) \(a_{33}=+0.278337210\) \(a_{34}=+0.326791538\) \(a_{35}=+0.392355387\)
\(a_{36}=-0.308779556\) \(a_{37}=+0.357764291\) \(a_{38}=+0.430152109\) \(a_{39}=-0.788749367\) \(a_{40}=+0.463747560\)
\(a_{41}=-1.341310228\) \(a_{42}=+0.069312181\) \(a_{43}=+0.574698305\) \(a_{44}=+0.446582489\) \(a_{45}=+0.295670473\)
\(a_{46}=+0.241385270\) \(a_{47}=-0.042142361\) \(a_{48}=-0.452897797\) \(a_{49}=-0.804340555\) \(a_{50}=+0.057866720\)
\(a_{51}=+0.695168988\) \(a_{52}=-1.265521255\) \(a_{53}=+1.300300337\) \(a_{54}=+0.052232150\) \(a_{55}=-0.427623050\)
\(a_{56}=+0.231261233\) \(a_{57}=+0.915043297\) \(a_{58}=-0.369296225\) \(a_{59}=-0.534754222\) \(a_{60}=+0.474393114\)
\(a_{61}=-1.388591964\) \(a_{62}=+0.286509568\) \(a_{63}=+0.147444696\) \(a_{64}=-0.584762280\) \(a_{65}=+1.211794177\)
\(a_{66}=-0.075542448\) \(a_{67}=-0.504438378\) \(a_{68}=+1.115374753\) \(a_{69}=+0.513488064\) \(a_{70}=-0.106487690\)
\(a_{71}=-1.014900833\) \(a_{72}=+0.174273427\) \(a_{73}=-1.481303439\) \(a_{74}=-0.097099451\) \(a_{75}=+0.123097280\)
\(a_{76}=+1.468155527\) \(a_{77}=-0.213246693\) \(a_{78}=+0.214071478\) \(a_{79}=-0.849946919\) \(a_{80}=+0.695809007\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.364039929\) \(a_{83}=+0.316181666\) \(a_{84}=+0.236569948\) \(a_{85}=-1.068022070\)
\(a_{86}=-0.155976691\) \(a_{87}=-0.785587304\) \(a_{88}=-0.252048620\) \(a_{89}=+0.079300998\) \(a_{90}=-0.080246803\)
\(a_{91}=+0.604296474\) \(a_{92}=+0.823873954\) \(a_{93}=+0.609478960\) \(a_{94}=+0.011437699\) \(a_{95}=-1.405825711\)
\(a_{96}=+0.424769707\) \(a_{97}=+0.441308292\) \(a_{98}=+0.218303024\) \(a_{99}=-0.160698063\) \(a_{100}=+0.197505356\)

Showing 100 of 1228 available coefficients

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