Properties

Level $61$
Weight $0$
Character 61.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 61 \)
Weight: \( 0 \)
Character: 61.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.21167434412 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.954153399\) \(a_{3}=+1.558622340\) \(a_{4}=+2.818715506\) \(a_{5}=-1.299171858\)
\(a_{6}=-3.045787143\) \(a_{7}=+0.645524019\) \(a_{8}=-3.554049087\) \(a_{9}=+1.429303599\) \(a_{10}=+2.538781103\)
\(a_{11}=-0.319825861\) \(a_{12}=+4.393312958\) \(a_{13}=+0.011188180\) \(a_{14}=-1.261452956\) \(a_{15}=-2.024918282\)
\(a_{16}=+4.126441597\) \(a_{17}=+1.158543500\) \(a_{18}=-2.793078486\) \(a_{19}=+0.715537884\) \(a_{20}=-3.661995862\)
\(a_{21}=+1.006128157\) \(a_{22}=+0.624988794\) \(a_{23}=+1.336919238\) \(a_{24}=-5.539420305\) \(a_{25}=+0.687847518\)
\(a_{26}=-0.021863421\) \(a_{27}=+0.669122180\) \(a_{28}=+1.819548562\) \(a_{29}=+0.746747505\) \(a_{30}=+3.957000943\)
\(a_{31}=+1.354681454\) \(a_{32}=-4.509650785\) \(a_{33}=-0.498487732\) \(a_{34}=-2.263971718\) \(a_{35}=-0.838646639\)
\(a_{36}=+4.028800217\) \(a_{37}=-0.183894937\) \(a_{38}=-1.398270787\) \(a_{39}=+0.017438148\) \(a_{40}=+4.617320558\)
\(a_{41}=+0.067547670\) \(a_{42}=-1.966128758\) \(a_{43}=+1.069163610\) \(a_{44}=-0.901498114\) \(a_{45}=-1.856911013\)
\(a_{46}=-2.612545273\) \(a_{47}=+1.029250434\) \(a_{48}=+6.431564058\) \(a_{49}=-0.583298741\) \(a_{50}=-1.344159565\)
\(a_{51}=+1.805731781\) \(a_{52}=+0.031536297\) \(a_{53}=-0.679350757\) \(a_{54}=-1.307567382\) \(a_{55}=+0.415508759\)
\(a_{56}=-2.294224050\) \(a_{57}=+1.115253331\) \(a_{58}=-1.459259174\) \(a_{59}=-0.418232680\) \(a_{60}=-5.707668560\)
\(a_{61}=+0.128036880\) \(a_{62}=-2.647255367\) \(a_{63}=+0.922649804\) \(a_{64}=+4.686107811\) \(a_{65}=-0.014535369\)
\(a_{66}=+0.974121496\) \(a_{67}=+0.532046504\) \(a_{68}=+3.265604527\) \(a_{69}=+2.083752191\) \(a_{70}=+1.638844181\)
\(a_{71}=+0.407379721\) \(a_{72}=-5.079815151\) \(a_{73}=-0.570129543\) \(a_{74}=+0.359358917\) \(a_{75}=+1.072094508\)
\(a_{76}=+2.016897727\) \(a_{77}=-0.206455275\) \(a_{78}=-0.034076816\) \(a_{79}=-0.290771391\) \(a_{80}=-5.360956799\)
\(a_{81}=-0.386394821\) \(a_{82}=-0.131998510\) \(a_{83}=-0.501002259\) \(a_{84}=+2.835989037\) \(a_{85}=-1.505147112\)
\(a_{86}=-2.089309702\) \(a_{87}=+1.163897343\) \(a_{88}=+1.136676810\) \(a_{89}=-0.898168626\) \(a_{90}=+3.628688967\)
\(a_{91}=+0.007222239\) \(a_{92}=+3.768394986\) \(a_{93}=+2.111436777\) \(a_{94}=-2.011313234\) \(a_{95}=-0.929606682\)
\(a_{96}=-7.028842459\) \(a_{97}=-1.919722360\) \(a_{98}=+1.139855217\) \(a_{99}=-0.457128255\) \(a_{100}=+1.938846464\)

Showing 100 of 546 available coefficients

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