Properties

Level $541$
Weight $0$
Character 541.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 541 \)
Weight: \( 0 \)
Character: 541.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.2947678788 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.733274681\) \(a_{3}=-1.002033520\) \(a_{4}=-0.462308296\) \(a_{5}=+1.491593530\)
\(a_{6}=+0.734765679\) \(a_{7}=+1.566387958\) \(a_{8}=+1.072273462\) \(a_{9}=+0.004071127\) \(a_{10}=-1.093747811\)
\(a_{11}=-1.344608489\) \(a_{12}=+0.463248319\) \(a_{13}=-0.002790288\) \(a_{14}=-1.148592775\) \(a_{15}=-1.494626548\)
\(a_{16}=-0.323962949\) \(a_{17}=+0.697055017\) \(a_{18}=-0.002985151\) \(a_{19}=+0.177791253\) \(a_{20}=-0.689575841\)
\(a_{21}=-1.569573144\) \(a_{22}=+0.985967463\) \(a_{23}=+0.097745015\) \(a_{24}=-1.074454005\) \(a_{25}=+1.224851559\)
\(a_{26}=+0.002046120\) \(a_{27}=+0.997954087\) \(a_{28}=-0.724154057\) \(a_{29}=-0.520067152\) \(a_{30}=+1.095972002\)
\(a_{31}=-0.182646026\) \(a_{32}=-0.834719797\) \(a_{33}=+1.347342756\) \(a_{34}=-0.511132855\) \(a_{35}=+2.336414524\)
\(a_{36}=-0.001882141\) \(a_{37}=+1.358765548\) \(a_{38}=-0.130369876\) \(a_{39}=+0.002795938\) \(a_{40}=+1.599396565\)
\(a_{41}=+0.362889847\) \(a_{42}=+1.150928342\) \(a_{43}=+1.581907225\) \(a_{44}=+0.621623627\) \(a_{45}=+0.006072271\)
\(a_{46}=-0.071673979\) \(a_{47}=+0.936285120\) \(a_{48}=+0.324621562\) \(a_{49}=+1.453571669\) \(a_{50}=-0.898152642\)
\(a_{51}=-0.698472365\) \(a_{52}=+0.001289949\) \(a_{53}=-0.725416600\) \(a_{54}=-0.731774465\) \(a_{55}=-2.005609495\)
\(a_{56}=+1.679596567\) \(a_{57}=-0.178152758\) \(a_{58}=+0.381352133\) \(a_{59}=-0.360679524\) \(a_{60}=+0.690978168\)
\(a_{61}=+0.867512487\) \(a_{62}=+0.133929751\) \(a_{63}=+0.006376767\) \(a_{64}=+0.936041678\) \(a_{65}=-0.004162129\)
\(a_{66}=-0.987972298\) \(a_{67}=+1.295805293\) \(a_{68}=-0.322254186\) \(a_{69}=-0.097943839\) \(a_{70}=-1.713233521\)
\(a_{71}=+0.143944961\) \(a_{72}=+0.004365278\) \(a_{73}=-1.331420694\) \(a_{74}=-0.996348470\) \(a_{75}=-1.227342260\)
\(a_{76}=-0.082194328\) \(a_{77}=-2.106178720\) \(a_{78}=-0.002050305\) \(a_{79}=-0.528609220\) \(a_{80}=-0.483220938\)
\(a_{81}=-1.004054449\) \(a_{82}=-0.266098004\) \(a_{83}=+1.611520015\) \(a_{84}=+0.725626484\) \(a_{85}=+1.039723016\)
\(a_{86}=-1.159972612\) \(a_{87}=+0.521124676\) \(a_{88}=-1.441788122\) \(a_{89}=+0.133667729\) \(a_{90}=-0.004452762\)
\(a_{91}=-0.004370879\) \(a_{92}=-0.045188385\) \(a_{93}=+0.183017387\) \(a_{94}=-0.686554149\) \(a_{95}=+0.265192399\)
\(a_{96}=+0.836416990\) \(a_{97}=-0.161833061\) \(a_{98}=-1.065867293\) \(a_{99}=-0.005473977\) \(a_{100}=-0.566258961\)

Showing 100 of 1596 available coefficients

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