Properties

Level $56$
Weight $0$
Character 56.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 56 = 2^{3} \cdot 7 \)
Weight: \( 0 \)
Character: 56.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.38278649078 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.026323650\) \(a_{4}=+0.000000000\) \(a_{5}=+0.705608667\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.377964473\) \(a_{8}=+0.000000000\) \(a_{9}=-0.999307065\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.524732847\) \(a_{12}=+0.000000000\) \(a_{13}=-1.344193366\) \(a_{14}=+0.000000000\) \(a_{15}=+0.018574195\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.827206174\) \(a_{18}=+0.000000000\) \(a_{19}=-0.721230527\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.009949404\) \(a_{22}=+0.000000000\) \(a_{23}=+1.515476775\) \(a_{24}=+0.000000000\) \(a_{25}=-0.502116409\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.052629059\) \(a_{28}=+0.000000000\) \(a_{29}=+0.581152625\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.021125605\) \(a_{32}=+0.000000000\) \(a_{33}=-0.013812884\) \(a_{34}=+0.000000000\) \(a_{35}=-0.266695008\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.501399053\) \(a_{38}=+0.000000000\) \(a_{39}=-0.035384075\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.480889532\) \(a_{42}=+0.000000000\) \(a_{43}=+0.056399171\) \(a_{44}=+0.000000000\) \(a_{45}=-0.705119726\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.917744427\) \(a_{48}=+0.000000000\) \(a_{49}=+0.142857143\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.021775085\) \(a_{52}=+0.000000000\) \(a_{53}=-1.070836431\) \(a_{54}=+0.000000000\) \(a_{55}=-0.370256044\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.018985420\) \(a_{58}=+0.000000000\) \(a_{59}=+0.710356268\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.121236199\) \(a_{62}=+0.000000000\) \(a_{63}=+0.377702568\) \(a_{64}=+0.000000000\) \(a_{65}=-0.948474489\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.721995804\) \(a_{68}=+0.000000000\) \(a_{69}=+0.039892880\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.769769846\) \(a_{72}=+0.000000000\) \(a_{73}=+1.659510680\) \(a_{74}=+0.000000000\) \(a_{75}=-0.013217536\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.198330374\) \(a_{78}=+0.000000000\) \(a_{79}=-1.437855337\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.997921677\) \(a_{82}=+0.000000000\) \(a_{83}=-0.654150432\) \(a_{84}=+0.000000000\) \(a_{85}=-0.583683845\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.015298058\) \(a_{88}=+0.000000000\) \(a_{89}=-0.632656244\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.508057337\) \(a_{92}=+0.000000000\) \(a_{93}=+0.000556103\) \(a_{94}=+0.000000000\) \(a_{95}=-0.508906511\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.514939627\) \(a_{98}=+0.000000000\) \(a_{99}=+0.524369241\) \(a_{100}=+0.000000000\)

Showing 100 of 400 available coefficients

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