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: \( 14.6262358404 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.555362003\) \(a_{3}=-0.577350269\) \(a_{4}=-0.691573046\) \(a_{5}=-0.952818339\)
\(a_{6}=-0.320638402\) \(a_{7}=+1.837441581\) \(a_{8}=-0.939435394\) \(a_{9}=+0.333333333\) \(a_{10}=-0.529159101\)
\(a_{11}=-0.015751614\) \(a_{12}=+0.399279877\) \(a_{13}=+1.030969914\) \(a_{14}=+1.020445096\) \(a_{15}=+0.550110579\)
\(a_{16}=+0.169843157\) \(a_{17}=+0.647842027\) \(a_{18}=+0.185041093\) \(a_{19}=+0.633395929\) \(a_{20}=+0.658943481\)
\(a_{21}=-1.060847391\) \(a_{22}=-0.008747849\) \(a_{23}=+0.209597276\) \(a_{24}=+0.542383278\) \(a_{25}=-0.092137213\)
\(a_{26}=+0.572561499\) \(a_{27}=-0.192450090\) \(a_{28}=-1.270725071\) \(a_{29}=+0.319618849\) \(a_{30}=+0.305510149\)
\(a_{31}=-0.201028820\) \(a_{32}=+1.033761589\) \(a_{33}=+0.009094200\) \(a_{34}=+0.359778147\) \(a_{35}=-1.750748034\)
\(a_{36}=-0.230524349\) \(a_{37}=+0.794543773\) \(a_{38}=+0.351764031\) \(a_{39}=-0.595230740\) \(a_{40}=+0.895111272\)
\(a_{41}=-0.175961490\) \(a_{42}=-0.589154332\) \(a_{43}=+0.779074946\) \(a_{44}=+0.010893393\) \(a_{45}=-0.317606113\)
\(a_{46}=+0.116402363\) \(a_{47}=-1.836426037\) \(a_{48}=-0.098060821\) \(a_{49}=+2.376191563\) \(a_{50}=-0.051169506\)
\(a_{51}=-0.374022729\) \(a_{52}=-0.712990985\) \(a_{53}=+1.344094164\) \(a_{54}=-0.106879461\) \(a_{55}=+0.015008428\)
\(a_{56}=-1.726157685\) \(a_{57}=-0.365691299\) \(a_{58}=+0.177504204\) \(a_{59}=+1.014962083\) \(a_{60}=-0.380441283\)
\(a_{61}=+0.708599800\) \(a_{62}=-0.111643486\) \(a_{63}=+0.612480712\) \(a_{64}=+0.404265478\) \(a_{65}=-0.982327011\)
\(a_{66}=+0.005050573\) \(a_{67}=-0.101217925\) \(a_{68}=-0.448019252\) \(a_{69}=-0.121011043\) \(a_{70}=-0.972298934\)
\(a_{71}=+1.030086297\) \(a_{72}=-0.313145133\) \(a_{73}=+0.953896293\) \(a_{74}=+0.441259424\) \(a_{75}=+0.053195447\)
\(a_{76}=-0.438039555\) \(a_{77}=-0.028942679\) \(a_{78}=-0.330568533\) \(a_{79}=+0.487897242\) \(a_{80}=-0.161832691\)
\(a_{81}=+0.111111097\) \(a_{82}=-0.097722335\) \(a_{83}=-1.294472244\) \(a_{84}=+0.733653484\) \(a_{85}=-0.617260849\)
\(a_{86}=+0.432668577\) \(a_{87}=-0.184532033\) \(a_{88}=+0.014797689\) \(a_{89}=+0.605476172\) \(a_{90}=-0.176386442\)
\(a_{91}=+1.894346799\) \(a_{92}=-0.144951771\) \(a_{93}=+0.116064264\) \(a_{94}=-1.019881159\) \(a_{95}=-0.603511605\)
\(a_{96}=-0.596842831\) \(a_{97}=-1.335322825\) \(a_{98}=+1.319647154\) \(a_{99}=-0.005250649\) \(a_{100}=+0.063718356\)

Showing 100 of 5000 available coefficients

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