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: \( 17.0740108048 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.832524228\) \(a_{3}=+0.577350270\) \(a_{4}=-0.306903410\) \(a_{5}=+0.671121252\)
\(a_{6}=-0.480658087\) \(a_{7}=-1.406826174\) \(a_{8}=+1.088028752\) \(a_{9}=+0.333333334\) \(a_{10}=-0.558724702\)
\(a_{11}=+1.249338444\) \(a_{12}=-0.177190767\) \(a_{13}=+0.421870823\) \(a_{14}=+1.171216874\) \(a_{15}=+0.387472036\)
\(a_{16}=-0.598906887\) \(a_{17}=-0.922402246\) \(a_{18}=-0.277508076\) \(a_{19}=-0.922014047\) \(a_{20}=-0.205969401\)
\(a_{21}=-0.812231471\) \(a_{22}=-1.040104523\) \(a_{23}=-0.672130938\) \(a_{24}=+0.628173694\) \(a_{25}=-0.549596266\)
\(a_{26}=-0.351217681\) \(a_{27}=+0.192450090\) \(a_{28}=+0.431759750\) \(a_{29}=-1.282674311\) \(a_{30}=-0.322579857\)
\(a_{31}=+0.939525046\) \(a_{32}=-0.589424259\) \(a_{33}=+0.721305887\) \(a_{34}=+0.767922218\) \(a_{35}=-0.944150942\)
\(a_{36}=-0.102301137\) \(a_{37}=-1.428799585\) \(a_{38}=+0.767599033\) \(a_{39}=+0.243567233\) \(a_{40}=+0.730199218\)
\(a_{41}=+0.322598965\) \(a_{42}=+0.676202378\) \(a_{43}=-1.717693736\) \(a_{44}=-0.383426229\) \(a_{45}=+0.223707084\)
\(a_{46}=+0.559565290\) \(a_{47}=-0.442554095\) \(a_{48}=-0.345779053\) \(a_{49}=+0.979159883\) \(a_{50}=+0.457552207\)
\(a_{51}=-0.532549186\) \(a_{52}=-0.129473594\) \(a_{53}=+0.108360536\) \(a_{54}=-0.160219363\) \(a_{55}=+0.838457580\)
\(a_{56}=-1.530667326\) \(a_{57}=-0.532325059\) \(a_{58}=+1.067857440\) \(a_{59}=-0.154639935\) \(a_{60}=-0.118916489\)
\(a_{61}=+1.382208988\) \(a_{62}=-0.782177364\) \(a_{63}=-0.468942059\) \(a_{64}=+1.089616863\) \(a_{65}=+0.283126474\)
\(a_{66}=-0.600504627\) \(a_{67}=-1.315216177\) \(a_{68}=+0.283088395\) \(a_{69}=-0.388054978\) \(a_{70}=+0.786028534\)
\(a_{71}=-1.231637022\) \(a_{72}=+0.362676251\) \(a_{73}=+1.466667097\) \(a_{74}=+1.189510271\) \(a_{75}=-0.317309552\)
\(a_{76}=+0.282969255\) \(a_{77}=-1.757602022\) \(a_{78}=-0.202775623\) \(a_{79}=-0.073681177\) \(a_{80}=-0.401939140\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.268571454\) \(a_{83}=+0.758447846\) \(a_{84}=+0.249276608\) \(a_{85}=-0.619043750\)
\(a_{86}=+1.430021652\) \(a_{87}=-0.740552359\) \(a_{88}=+1.359316148\) \(a_{89}=-1.123239852\) \(a_{90}=-0.186241568\)
\(a_{91}=-0.593498915\) \(a_{92}=+0.206279277\) \(a_{93}=+0.542435039\) \(a_{94}=+0.368437006\) \(a_{95}=-0.618783221\)
\(a_{96}=-0.340304255\) \(a_{97}=-0.199206023\) \(a_{98}=-0.815174326\) \(a_{99}=+0.416446149\) \(a_{100}=+0.168672968\)

Showing 100 of 1228 available coefficients

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