Properties

Level $59$
Weight $0$
Character 59.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 59 \)
Weight: \( 0 \)
Character: 59.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.5985969867 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.306076394\) \(a_{3}=-1.450712311\) \(a_{4}=-0.906317241\) \(a_{5}=-0.738868768\)
\(a_{6}=+0.444028792\) \(a_{7}=+0.503833289\) \(a_{8}=+0.583478706\) \(a_{9}=+1.104566208\) \(a_{10}=+0.226150288\)
\(a_{11}=-1.142274838\) \(a_{12}=+1.314805579\) \(a_{13}=-0.640238381\) \(a_{14}=-0.154211476\) \(a_{15}=+1.071886018\)
\(a_{16}=+0.727728183\) \(a_{17}=-0.096087117\) \(a_{18}=-0.338081641\) \(a_{19}=-1.294195633\) \(a_{20}=+0.669649504\)
\(a_{21}=-0.730917155\) \(a_{22}=+0.349623363\) \(a_{23}=+1.039893792\) \(a_{24}=-0.846459742\) \(a_{25}=-0.454072943\)
\(a_{26}=+0.195961855\) \(a_{27}=-0.151695485\) \(a_{28}=-0.456632797\) \(a_{29}=+0.049042459\) \(a_{30}=-0.328079007\)
\(a_{31}=-0.478345830\) \(a_{32}=-0.806219124\) \(a_{33}=+1.657112170\) \(a_{34}=+0.029409998\) \(a_{35}=-0.372266682\)
\(a_{36}=-1.001087399\) \(a_{37}=-0.813470323\) \(a_{38}=+0.396122732\) \(a_{39}=+0.928801701\) \(a_{40}=-0.431114193\)
\(a_{41}=-1.124885173\) \(a_{42}=+0.223716487\) \(a_{43}=+1.297103982\) \(a_{44}=+1.035263380\) \(a_{45}=-0.816129474\)
\(a_{46}=-0.318286941\) \(a_{47}=+0.954250176\) \(a_{48}=-1.055724234\) \(a_{49}=-0.746152017\) \(a_{50}=+0.138981009\)
\(a_{51}=+0.139394763\) \(a_{52}=+0.580259083\) \(a_{53}=+0.340542782\) \(a_{54}=+0.046430407\) \(a_{55}=+0.843991203\)
\(a_{56}=+0.293975996\) \(a_{57}=+1.877505538\) \(a_{58}=-0.015010739\) \(a_{59}=-0.130188911\) \(a_{60}=-0.971468779\)
\(a_{61}=+1.774040307\) \(a_{62}=+0.146410367\) \(a_{63}=+0.556517226\) \(a_{64}=-0.480963541\) \(a_{65}=+0.473052144\)
\(a_{66}=-0.507202917\) \(a_{67}=-1.097951118\) \(a_{68}=+0.087085411\) \(a_{69}=-1.508586725\) \(a_{70}=+0.113942043\)
\(a_{71}=-1.439389531\) \(a_{72}=+0.644490862\) \(a_{73}=-0.027989398\) \(a_{74}=+0.248984063\) \(a_{75}=+0.658729208\)
\(a_{76}=+1.172951816\) \(a_{77}=-0.575516089\) \(a_{78}=-0.284284275\) \(a_{79}=-0.516942330\) \(a_{80}=-0.537695626\)
\(a_{81}=-0.884499700\) \(a_{82}=+0.344300797\) \(a_{83}=-0.995965823\) \(a_{84}=+0.662442819\) \(a_{85}=+0.070995770\)
\(a_{86}=-0.397012909\) \(a_{87}=-0.071146500\) \(a_{88}=-0.666493045\) \(a_{89}=-0.369453587\) \(a_{90}=+0.249797966\)
\(a_{91}=-0.322573409\) \(a_{92}=-0.942473673\) \(a_{93}=+0.693942185\) \(a_{94}=-0.292073453\) \(a_{95}=+0.956240734\)
\(a_{96}=+1.169592008\) \(a_{97}=+0.876477239\) \(a_{98}=+0.228379518\) \(a_{99}=-1.261718187\) \(a_{100}=+0.411534137\)

Showing 100 of 546 available coefficients

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