Properties

Level $499$
Weight $0$
Character 499.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 499 \)
Weight: \( 0 \)
Character: 499.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.62907560949 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.430434496\) \(a_{3}=-1.591369647\) \(a_{4}=-0.814726148\) \(a_{5}=+0.468998858\)
\(a_{6}=+0.684980390\) \(a_{7}=+0.056255638\) \(a_{8}=+0.781120747\) \(a_{9}=+1.532457356\) \(a_{10}=-0.201873291\)
\(a_{11}=+0.270219271\) \(a_{12}=+1.296530456\) \(a_{13}=+0.378785617\) \(a_{14}=-0.024214360\) \(a_{15}=-0.746350539\)
\(a_{16}=+0.478504839\) \(a_{17}=+0.854000698\) \(a_{18}=-0.659622520\) \(a_{19}=-1.072530576\) \(a_{20}=-0.382105642\)
\(a_{21}=-0.089523538\) \(a_{22}=-0.116311673\) \(a_{23}=-0.311494169\) \(a_{24}=-1.243051823\) \(a_{25}=-0.780040083\)
\(a_{26}=-0.163042399\) \(a_{27}=-0.847336484\) \(a_{28}=-0.045832927\) \(a_{29}=-0.679625098\) \(a_{30}=+0.321255028\)
\(a_{31}=+0.799940448\) \(a_{32}=-0.987085726\) \(a_{33}=-0.430018775\) \(a_{34}=-0.367591348\) \(a_{35}=+0.026383843\)
\(a_{36}=-1.248533086\) \(a_{37}=-1.457826556\) \(a_{38}=+0.461654151\) \(a_{39}=-0.602787940\) \(a_{40}=+0.366344746\)
\(a_{41}=+1.550703432\) \(a_{42}=+0.038534008\) \(a_{43}=-1.898095356\) \(a_{44}=-0.220154716\) \(a_{45}=+0.718720751\)
\(a_{46}=+0.134077821\) \(a_{47}=-0.069788665\) \(a_{48}=-0.761478085\) \(a_{49}=-0.996835310\) \(a_{50}=+0.335756162\)
\(a_{51}=-1.359030792\) \(a_{52}=-0.308606563\) \(a_{53}=+0.753743825\) \(a_{54}=+0.364722860\) \(a_{55}=+0.126732549\)
\(a_{56}=+0.043942434\) \(a_{57}=+1.706792600\) \(a_{58}=+0.292534095\) \(a_{59}=+0.410354772\) \(a_{60}=+0.608071305\)
\(a_{61}=-1.781866896\) \(a_{62}=-0.344321956\) \(a_{63}=+0.086209378\) \(a_{64}=-0.053629086\) \(a_{65}=+0.177650014\)
\(a_{66}=+0.185094920\) \(a_{67}=+1.266447473\) \(a_{68}=-0.695776693\) \(a_{69}=+0.495702358\) \(a_{70}=-0.011356512\)
\(a_{71}=-1.156836051\) \(a_{72}=+1.197034226\) \(a_{73}=+0.082163386\) \(a_{74}=+0.627498855\) \(a_{75}=+1.241332107\)
\(a_{76}=+0.873818685\) \(a_{77}=+0.015201381\) \(a_{78}=+0.259460719\) \(a_{79}=+0.364271570\) \(a_{80}=+0.224418214\)
\(a_{81}=-0.184031792\) \(a_{82}=-0.667476284\) \(a_{83}=-0.099901434\) \(a_{84}=+0.072937153\) \(a_{85}=+0.400525345\)
\(a_{86}=+0.817005712\) \(a_{87}=+1.081534792\) \(a_{88}=+0.211073856\) \(a_{89}=-1.846296199\) \(a_{90}=-0.309362202\)
\(a_{91}=+0.021308845\) \(a_{92}=+0.253782431\) \(a_{93}=-1.273000973\) \(a_{94}=+0.030039453\) \(a_{95}=-0.503015625\)
\(a_{96}=+1.570818259\) \(a_{97}=+1.287804438\) \(a_{98}=+0.429072321\) \(a_{99}=+0.414099507\) \(a_{100}=+0.635519051\)

Showing 100 of 1558 available coefficients

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