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: \( 28.102435957 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.522739978\) \(a_{3}=-0.577350269\) \(a_{4}=-0.726742915\) \(a_{5}=+1.278873525\)
\(a_{6}=+0.301804067\) \(a_{7}=-0.878091759\) \(a_{8}=+0.902637554\) \(a_{9}=+0.333333333\) \(a_{10}=-0.668518319\)
\(a_{11}=-1.700469824\) \(a_{12}=+0.419585218\) \(a_{13}=-0.175159666\) \(a_{14}=+0.459013667\) \(a_{15}=-0.738357974\)
\(a_{16}=+0.254898180\) \(a_{17}=+1.720305217\) \(a_{18}=-0.174246659\) \(a_{19}=+0.585146881\) \(a_{20}=-0.929412274\)
\(a_{21}=+0.506966513\) \(a_{22}=+0.888903559\) \(a_{23}=-0.324421891\) \(a_{24}=-0.521138035\) \(a_{25}=+0.635517494\)
\(a_{26}=+0.091562960\) \(a_{27}=-0.192450090\) \(a_{28}=+0.638146965\) \(a_{29}=+0.709851014\) \(a_{30}=+0.385969231\)
\(a_{31}=+1.275133763\) \(a_{32}=-1.035883023\) \(a_{33}=+0.981766710\) \(a_{34}=-0.899272312\) \(a_{35}=-1.122968303\)
\(a_{36}=-0.242247638\) \(a_{37}=+0.854426195\) \(a_{38}=-0.305879668\) \(a_{39}=+0.101128480\) \(a_{40}=+1.154359271\)
\(a_{41}=-0.483019864\) \(a_{42}=-0.265011664\) \(a_{43}=+1.097534911\) \(a_{44}=+1.235804397\) \(a_{45}=+0.426291175\)
\(a_{46}=+0.169588292\) \(a_{47}=-1.455798145\) \(a_{48}=-0.147165533\) \(a_{49}=-0.228954863\) \(a_{50}=-0.332210401\)
\(a_{51}=-0.993218680\) \(a_{52}=+0.127296046\) \(a_{53}=-0.407969358\) \(a_{54}=+0.100601356\) \(a_{55}=-2.174685838\)
\(a_{56}=-0.792598597\) \(a_{57}=-0.337834709\) \(a_{58}=-0.371067504\) \(a_{59}=-0.887415494\) \(a_{60}=+0.536596427\)
\(a_{61}=-0.481681690\) \(a_{62}=-0.666563396\) \(a_{63}=-0.292697253\) \(a_{64}=+0.286599289\) \(a_{65}=-0.224007059\)
\(a_{66}=-0.513208709\) \(a_{67}=-0.338239685\) \(a_{68}=-1.250219628\) \(a_{69}=+0.187305066\) \(a_{70}=+0.587020426\)
\(a_{71}=+0.640440767\) \(a_{72}=+0.300879185\) \(a_{73}=-0.459118711\) \(a_{74}=-0.446642730\) \(a_{75}=-0.366916196\)
\(a_{76}=-0.425251350\) \(a_{77}=+1.493168539\) \(a_{78}=-0.052863900\) \(a_{79}=-1.932806711\) \(a_{80}=+0.325982534\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.252493793\) \(a_{83}=+0.364883775\) \(a_{84}=-0.368434322\) \(a_{85}=+2.200052797\)
\(a_{86}=-0.573725375\) \(a_{87}=-0.409832674\) \(a_{88}=-1.534907922\) \(a_{89}=+0.137017154\) \(a_{90}=-0.222839440\)
\(a_{91}=+0.153806259\) \(a_{92}=+0.235771311\) \(a_{93}=-0.736198821\) \(a_{94}=+0.761003891\) \(a_{95}=+0.748328855\)
\(a_{96}=+0.598067342\) \(a_{97}=-0.231301748\) \(a_{98}=+0.119683860\) \(a_{99}=-0.566823275\) \(a_{100}=-0.461857836\)

Showing 100 of 1228 available coefficients

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