Properties

Level $293$
Weight $0$
Character 293.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 293 \)
Weight: \( 0 \)
Character: 293.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.85049092038 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.816908353\) \(a_{3}=-1.175456744\) \(a_{4}=+2.301155953\) \(a_{5}=-0.336465858\)
\(a_{6}=-2.135697106\) \(a_{7}=-1.435088332\) \(a_{8}=+2.364081181\) \(a_{9}=+0.381698497\) \(a_{10}=-0.611327657\)
\(a_{11}=-0.572227980\) \(a_{12}=-2.704909286\) \(a_{13}=+1.559518975\) \(a_{14}=-2.607423991\) \(a_{15}=+0.395501101\)
\(a_{16}=+1.994162853\) \(a_{17}=+1.806622518\) \(a_{18}=+0.693511216\) \(a_{19}=-0.400743593\) \(a_{20}=-0.774260442\)
\(a_{21}=+1.686884227\) \(a_{22}=-1.039685791\) \(a_{23}=-0.520038554\) \(a_{24}=-2.778875142\) \(a_{25}=-0.886790763\)
\(a_{26}=+2.833502982\) \(a_{27}=+0.726786639\) \(a_{28}=-3.302362089\) \(a_{29}=-0.616460787\) \(a_{30}=+0.718589253\)
\(a_{31}=+1.298240146\) \(a_{32}=+1.259129930\) \(a_{33}=+0.672629227\) \(a_{34}=+3.282467549\) \(a_{35}=+0.482858222\)
\(a_{36}=+0.878347823\) \(a_{37}=+0.679236365\) \(a_{38}=-0.728114376\) \(a_{39}=-1.833147075\) \(a_{40}=-0.795432572\)
\(a_{41}=+0.044984253\) \(a_{42}=+3.064914092\) \(a_{43}=-0.683836140\) \(a_{44}=-1.316785842\) \(a_{45}=-0.128428557\)
\(a_{46}=-0.944862356\) \(a_{47}=-1.515953253\) \(a_{48}=-2.344052099\) \(a_{49}=+1.059478519\) \(a_{50}=-1.611217537\)
\(a_{51}=-2.123606632\) \(a_{52}=+3.588696366\) \(a_{53}=+1.745266108\) \(a_{54}=+1.320504730\) \(a_{55}=+0.192535212\)
\(a_{56}=-3.392665215\) \(a_{57}=+0.471056705\) \(a_{58}=-1.120052772\) \(a_{59}=+0.601208674\) \(a_{60}=+0.910109659\)
\(a_{61}=-1.173037329\) \(a_{62}=+2.358783350\) \(a_{63}=-0.547771074\) \(a_{64}=+0.293560861\) \(a_{65}=-0.524724881\)
\(a_{66}=+1.222105660\) \(a_{67}=+1.050871111\) \(a_{68}=+4.157320153\) \(a_{69}=+0.611282790\) \(a_{70}=+0.877309096\)
\(a_{71}=-1.002221896\) \(a_{72}=+0.902366275\) \(a_{73}=-0.273758210\) \(a_{74}=+1.234110193\) \(a_{75}=+1.042384202\)
\(a_{76}=-0.922173537\) \(a_{77}=+0.821197672\) \(a_{78}=-3.330660203\) \(a_{79}=+1.259374725\) \(a_{80}=-0.670967683\)
\(a_{81}=-1.236004734\) \(a_{82}=+0.081732194\) \(a_{83}=+1.449412113\) \(a_{84}=+3.881783713\) \(a_{85}=-0.607866793\)
\(a_{86}=-1.242467602\) \(a_{87}=+0.724622903\) \(a_{88}=-1.352793369\) \(a_{89}=-0.728373424\) \(a_{90}=-0.233342880\)
\(a_{91}=-2.238047409\) \(a_{92}=-1.196689795\) \(a_{93}=-1.526025051\) \(a_{94}=-2.754348051\) \(a_{95}=+0.134836593\)
\(a_{96}=-1.480052809\) \(a_{97}=-0.105332610\) \(a_{98}=+1.924975269\) \(a_{99}=-0.218418551\) \(a_{100}=-2.040643862\)

Showing 100 of 936 available coefficients

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