Properties

Level $37$
Weight $0$
Character 37.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 37 \)
Weight: \( 0 \)
Character: 37.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.8257891651 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.765117899\) \(a_{3}=+0.133217337\) \(a_{4}=+2.115641198\) \(a_{5}=+1.037827461\)
\(a_{6}=+0.235144307\) \(a_{7}=+0.209695677\) \(a_{8}=+1.969238247\) \(a_{9}=-0.982253141\) \(a_{10}=+1.831887828\)
\(a_{11}=+1.345093458\) \(a_{12}=+0.281840087\) \(a_{13}=-1.492800290\) \(a_{14}=+0.370137594\) \(a_{15}=+0.138256611\)
\(a_{16}=+1.360296480\) \(a_{17}=-1.162071311\) \(a_{18}=-1.733792601\) \(a_{19}=+0.795088284\) \(a_{20}=+2.195670534\)
\(a_{21}=+0.027935100\) \(a_{22}=+2.374248539\) \(a_{23}=+0.508325341\) \(a_{24}=+0.262336676\) \(a_{25}=+0.077085840\)
\(a_{26}=-2.634968511\) \(a_{27}=-0.264070485\) \(a_{28}=+0.443640815\) \(a_{29}=-0.014362225\) \(a_{30}=+0.244039219\)
\(a_{31}=-1.103168098\) \(a_{32}=+0.431845418\) \(a_{33}=+0.179189769\) \(a_{34}=-2.051192871\) \(a_{35}=+0.217627933\)
\(a_{36}=-2.078095212\) \(a_{37}=-0.164398987\) \(a_{38}=+1.403424562\) \(a_{39}=-0.198866880\) \(a_{40}=+2.043729531\)
\(a_{41}=+0.532885917\) \(a_{42}=+0.049308745\) \(a_{43}=-1.080220554\) \(a_{44}=+2.845735135\) \(a_{45}=-1.019409284\)
\(a_{46}=+0.897254157\) \(a_{47}=+1.508752756\) \(a_{48}=+0.181215075\) \(a_{49}=-0.956027723\) \(a_{50}=+0.136065596\)
\(a_{51}=-0.154808046\) \(a_{52}=-3.158229793\) \(a_{53}=+1.557392195\) \(a_{54}=-0.466115539\) \(a_{55}=+1.395974929\)
\(a_{56}=+0.412940748\) \(a_{57}=+0.105919545\) \(a_{58}=-0.025351020\) \(a_{59}=-0.281702471\) \(a_{60}=+0.292501382\)
\(a_{61}=+0.312271375\) \(a_{62}=-1.947221759\) \(a_{63}=-0.205974240\) \(a_{64}=-0.598038401\) \(a_{65}=-1.549269135\)
\(a_{66}=+0.316291067\) \(a_{67}=+0.949320345\) \(a_{68}=-2.458525930\) \(a_{69}=+0.067717741\) \(a_{70}=+0.384138952\)
\(a_{71}=+1.182684056\) \(a_{72}=-1.934290452\) \(a_{73}=+1.224824981\) \(a_{74}=-0.290183596\) \(a_{75}=+0.010269166\)
\(a_{76}=+1.682121539\) \(a_{77}=+0.282060280\) \(a_{78}=-0.351023483\) \(a_{79}=-1.424283427\) \(a_{80}=+1.411753034\)
\(a_{81}=+0.947074379\) \(a_{82}=+0.940606449\) \(a_{83}=+1.266425204\) \(a_{84}=+0.059100647\) \(a_{85}=-1.206029525\)
\(a_{86}=-1.906716636\) \(a_{87}=-0.001913339\) \(a_{88}=+2.648809527\) \(a_{89}=+0.731264436\) \(a_{90}=-1.799377563\)
\(a_{91}=-0.313033779\) \(a_{92}=+1.075434031\) \(a_{93}=-0.146961113\) \(a_{94}=+2.663126485\) \(a_{95}=+0.825164479\)
\(a_{96}=+0.057529308\) \(a_{97}=-1.345608713\) \(a_{98}=-1.687501647\) \(a_{99}=-1.321222279\) \(a_{100}=+0.163085990\)

Showing 100 of 2000 available coefficients

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