Properties

Level $55$
Weight $0$
Character 55.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 55 = 5 \cdot 11 \)
Weight: \( 0 \)
Character: 55.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 1.68144381509 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.443283118\) \(a_{3}=-1.312125868\) \(a_{4}=+1.083066158\) \(a_{5}=+0.447213596\)
\(a_{6}=+1.893769114\) \(a_{7}=-0.408755701\) \(a_{8}=-0.119887984\) \(a_{9}=+0.721674293\) \(a_{10}=-0.645455832\)
\(a_{11}=-0.301511345\) \(a_{12}=-1.421119123\) \(a_{13}=-1.213703950\) \(a_{14}=+0.589950203\) \(a_{15}=-0.586800527\)
\(a_{16}=-0.910033855\) \(a_{17}=+1.573284321\) \(a_{18}=-1.041580324\) \(a_{19}=-0.126152387\) \(a_{20}=+0.484361911\)
\(a_{21}=+0.536338929\) \(a_{22}=+0.435166233\) \(a_{23}=-1.780111940\) \(a_{24}=+0.157308125\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.751718421\) \(a_{27}=+0.365198360\) \(a_{28}=-0.442709467\) \(a_{29}=+0.848173728\) \(a_{30}=+0.846919294\)
\(a_{31}=-0.911974494\) \(a_{32}=+1.433324484\) \(a_{33}=+0.395620835\) \(a_{34}=-2.270694700\) \(a_{35}=-0.182801107\)
\(a_{36}=+0.781621004\) \(a_{37}=-0.689672926\) \(a_{38}=+0.182073611\) \(a_{39}=+1.592532348\) \(a_{40}=-0.053615536\)
\(a_{41}=-0.270367151\) \(a_{42}=-0.774088922\) \(a_{43}=-0.472918362\) \(a_{44}=-0.326556734\) \(a_{45}=+0.322742555\)
\(a_{46}=+2.569205510\) \(a_{47}=-1.680549486\) \(a_{48}=+1.194078962\) \(a_{49}=-0.832918777\) \(a_{50}=-0.288656624\)
\(a_{51}=-2.064347055\) \(a_{52}=-1.314521674\) \(a_{53}=+0.306696656\) \(a_{54}=-0.527084627\) \(a_{55}=-0.134839972\)
\(a_{56}=+0.049004897\) \(a_{57}=+0.165527811\) \(a_{58}=-1.224154822\) \(a_{59}=+0.288549205\) \(a_{60}=-0.635543793\)
\(a_{61}=+1.067962632\) \(a_{62}=+1.316237392\) \(a_{63}=-0.294988482\) \(a_{64}=-1.158659175\) \(a_{65}=-0.542784907\)
\(a_{66}=-0.570992872\) \(a_{67}=+1.941713232\) \(a_{68}=+1.703971005\) \(a_{69}=+2.335730924\) \(a_{70}=+0.263833751\)
\(a_{71}=-0.072473742\) \(a_{72}=-0.086520076\) \(a_{73}=+0.088794611\) \(a_{74}=+0.995393291\) \(a_{75}=-0.262425174\)
\(a_{76}=-0.136631381\) \(a_{77}=+0.123244481\) \(a_{78}=-2.298475053\) \(a_{79}=-0.860650319\) \(a_{80}=-0.406979512\)
\(a_{81}=-1.200860508\) \(a_{82}=+0.390216345\) \(a_{83}=-0.446453006\) \(a_{84}=+0.580890544\) \(a_{85}=+0.703594138\)
\(a_{86}=+0.682555089\) \(a_{87}=-1.112910688\) \(a_{88}=+0.036147587\) \(a_{89}=+0.683501086\) \(a_{90}=-0.465808882\)
\(a_{91}=+0.496108409\) \(a_{92}=-1.927979000\) \(a_{93}=+1.196625325\) \(a_{94}=+2.425508702\) \(a_{95}=-0.056417063\)
\(a_{96}=-1.880702132\) \(a_{97}=-1.846922753\) \(a_{98}=+1.202137609\) \(a_{99}=-0.217592987\) \(a_{100}=+0.216613232\)

Showing 100 of 520 available coefficients

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