Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 21.4346433457 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.213657576\) \(a_{3}=-0.577350269\) \(a_{4}=+0.472964711\) \(a_{5}=+1.378703606\)
\(a_{6}=+0.700705528\) \(a_{7}=+1.441704792\) \(a_{8}=+0.639640371\) \(a_{9}=+0.333333333\) \(a_{10}=-1.673274075\)
\(a_{11}=+1.332908115\) \(a_{12}=-0.273066303\) \(a_{13}=+0.764412785\) \(a_{14}=-1.749735942\) \(a_{15}=-0.795994898\)
\(a_{16}=-1.249269093\) \(a_{17}=+0.017161826\) \(a_{18}=-0.404552525\) \(a_{19}=+0.048194799\) \(a_{20}=+0.652078152\)
\(a_{21}=-0.832368650\) \(a_{22}=-1.617694031\) \(a_{23}=+0.059040595\) \(a_{24}=-0.369296541\) \(a_{25}=+0.900823632\)
\(a_{26}=-0.927735367\) \(a_{27}=-0.192450090\) \(a_{28}=+0.681875490\) \(a_{29}=+1.102553508\) \(a_{30}=+0.966065238\)
\(a_{31}=+0.934443128\) \(a_{32}=+0.876544528\) \(a_{33}=-0.769554859\) \(a_{34}=-0.020828580\) \(a_{35}=+1.987683594\)
\(a_{36}=+0.157654904\) \(a_{37}=+0.866072493\) \(a_{38}=-0.058491983\) \(a_{39}=-0.441333927\) \(a_{40}=+0.881874486\)
\(a_{41}=-1.124357097\) \(a_{42}=+1.010210517\) \(a_{43}=-0.418684671\) \(a_{44}=+0.630418501\) \(a_{45}=+0.459567869\)
\(a_{46}=-0.071655065\) \(a_{47}=-1.215120411\) \(a_{48}=+0.721265847\) \(a_{49}=+1.078512706\) \(a_{50}=-1.093291425\)
\(a_{51}=-0.009908385\) \(a_{52}=+0.361540272\) \(a_{53}=-1.670820445\) \(a_{54}=+0.233568509\) \(a_{55}=+1.837685224\)
\(a_{56}=+0.922172588\) \(a_{57}=-0.027825280\) \(a_{58}=-1.338122418\) \(a_{59}=-0.707212074\) \(a_{60}=-0.376477497\)
\(a_{61}=+0.941327657\) \(a_{62}=-1.134093982\) \(a_{63}=+0.480568264\) \(a_{64}=+0.185444187\) \(a_{65}=+1.053898663\)
\(a_{66}=+0.933976084\) \(a_{67}=-0.798423156\) \(a_{68}=+0.008116938\) \(a_{69}=-0.034087103\) \(a_{70}=-2.412367252\)
\(a_{71}=+0.789501757\) \(a_{72}=+0.213213457\) \(a_{73}=+1.464474242\) \(a_{74}=-1.051115442\) \(a_{75}=-0.520090766\)
\(a_{76}=+0.022794439\) \(a_{77}=+1.921660016\) \(a_{78}=+0.535628264\) \(a_{79}=-0.775635270\) \(a_{80}=-1.722371803\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.364584508\) \(a_{83}=-0.695779153\) \(a_{84}=-0.393680998\) \(a_{85}=+0.023661071\)
\(a_{86}=+0.508139822\) \(a_{87}=-0.636559565\) \(a_{88}=+0.852581841\) \(a_{89}=-0.591317018\) \(a_{90}=-0.557758025\)
\(a_{91}=+1.102057575\) \(a_{92}=+0.027924118\) \(a_{93}=-0.539500992\) \(a_{94}=+1.474740092\) \(a_{95}=+0.066446343\)
\(a_{96}=-0.506073219\) \(a_{97}=-0.475633373\) \(a_{98}=-1.308945116\) \(a_{99}=+0.444302705\) \(a_{100}=+0.426057789\)

Showing 100 of 1228 available coefficients

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