Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 14.6012532084 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.783692408\) \(a_{3}=+0.577350269\) \(a_{4}=+2.181558607\) \(a_{5}=+1.296747659\)
\(a_{6}=-1.029815292\) \(a_{7}=-0.244028182\) \(a_{8}=-2.107537116\) \(a_{9}=+0.333333333\) \(a_{10}=-2.312998955\)
\(a_{11}=+0.684557899\) \(a_{12}=+1.259523453\) \(a_{13}=+0.012422889\) \(a_{14}=+0.435271291\) \(a_{15}=+0.748677262\)
\(a_{16}=+1.577641005\) \(a_{17}=+0.447145935\) \(a_{18}=-0.594524387\) \(a_{19}=-1.284150943\) \(a_{20}=+2.828931017\)
\(a_{21}=-0.140889737\) \(a_{22}=-1.221040730\) \(a_{23}=+1.139632703\) \(a_{24}=-1.216787121\) \(a_{25}=+0.681554492\)
\(a_{26}=-0.022158643\) \(a_{27}=+0.192450090\) \(a_{28}=-0.532361781\) \(a_{29}=+1.238535195\) \(a_{30}=-1.335410569\)
\(a_{31}=+1.036149308\) \(a_{32}=-0.706486210\) \(a_{33}=+0.395229688\) \(a_{34}=-0.797585071\) \(a_{35}=-0.316442974\)
\(a_{36}=+0.727186202\) \(a_{37}=-0.096655300\) \(a_{38}=+2.290530288\) \(a_{39}=+0.007172368\) \(a_{40}=-2.732943822\)
\(a_{41}=-1.358794871\) \(a_{42}=+0.251303954\) \(a_{43}=+1.452559519\) \(a_{44}=+1.493403179\) \(a_{45}=+0.432249220\)
\(a_{46}=-2.032754200\) \(a_{47}=+0.635108643\) \(a_{48}=+0.910850502\) \(a_{49}=-0.940450246\) \(a_{50}=-1.215683572\)
\(a_{51}=+0.258164442\) \(a_{52}=+0.027101296\) \(a_{53}=+0.930393238\) \(a_{54}=-0.343271762\) \(a_{55}=+0.887698857\)
\(a_{56}=+0.514298448\) \(a_{57}=-0.741404897\) \(a_{58}=-2.209165822\) \(a_{59}=+1.119575655\) \(a_{60}=+1.633284081\)
\(a_{61}=+0.647110553\) \(a_{62}=-1.848171662\) \(a_{63}=-0.081342672\) \(a_{64}=-0.317485179\) \(a_{65}=+0.016109374\)
\(a_{66}=-0.704968194\) \(a_{67}=+0.400969759\) \(a_{68}=+0.975492505\) \(a_{69}=+0.657967248\) \(a_{70}=+0.564436930\)
\(a_{71}=-0.408895547\) \(a_{72}=-0.702512372\) \(a_{73}=+0.283805503\) \(a_{74}=+0.172403325\) \(a_{75}=+0.393495669\)
\(a_{76}=-2.801450543\) \(a_{77}=-0.167051419\) \(a_{78}=-0.012793297\) \(a_{79}=+0.218320777\) \(a_{80}=+2.045800128\)
\(a_{81}=+0.111111109\) \(a_{82}=+2.423672100\) \(a_{83}=-1.614785489\) \(a_{84}=-0.307359219\) \(a_{85}=+0.579845803\)
\(a_{86}=-2.590919387\) \(a_{87}=+0.715068641\) \(a_{88}=-1.442731175\) \(a_{89}=+1.327048236\) \(a_{90}=-0.770999679\)
\(a_{91}=-0.003031526\) \(a_{92}=+2.486175568\) \(a_{93}=+0.598221091\) \(a_{94}=-1.132838519\) \(a_{95}=-1.665219783\)
\(a_{96}=-0.407889918\) \(a_{97}=+0.071486902\) \(a_{98}=+1.677473930\) \(a_{99}=+0.228185754\) \(a_{100}=+1.486851057\)

Showing 100 of 5000 available coefficients

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