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: \( 25.3431954147 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.358780846\) \(a_{3}=+0.577350269\) \(a_{4}=-0.871276304\) \(a_{5}=+0.544905122\)
\(a_{6}=-0.207142218\) \(a_{7}=-1.656544924\) \(a_{8}=+0.671378096\) \(a_{9}=+0.333333333\) \(a_{10}=-0.195501521\)
\(a_{11}=-0.621066783\) \(a_{12}=-0.503031609\) \(a_{13}=-0.459999866\) \(a_{14}=+0.594336589\) \(a_{15}=+0.314601119\)
\(a_{16}=+0.630398703\) \(a_{17}=-0.528252588\) \(a_{18}=-0.119593615\) \(a_{19}=+1.707135231\) \(a_{20}=-0.474762921\)
\(a_{21}=-0.956406658\) \(a_{22}=+0.222826866\) \(a_{23}=-1.140778674\) \(a_{24}=+0.387620324\) \(a_{25}=-0.703078408\)
\(a_{26}=+0.165039141\) \(a_{27}=+0.192450090\) \(a_{28}=+1.443308339\) \(a_{29}=-0.354966308\) \(a_{30}=-0.112872856\)
\(a_{31}=-0.409692913\) \(a_{32}=-0.897553076\) \(a_{33}=-0.358573074\) \(a_{34}=+0.189526911\) \(a_{35}=-0.902659814\)
\(a_{36}=-0.290425435\) \(a_{37}=+0.979582020\) \(a_{38}=-0.612487423\) \(a_{39}=-0.265581046\) \(a_{40}=+0.365837363\)
\(a_{41}=+1.915940240\) \(a_{42}=+0.343140390\) \(a_{43}=+0.889659475\) \(a_{44}=+0.541120771\) \(a_{45}=+0.181635041\)
\(a_{46}=+0.409289538\) \(a_{47}=+0.292234309\) \(a_{48}=+0.363960861\) \(a_{49}=+1.744141085\) \(a_{50}=+0.252251066\)
\(a_{51}=-0.304986774\) \(a_{52}=+0.400786983\) \(a_{53}=+0.791678749\) \(a_{54}=-0.069047406\) \(a_{55}=-0.338422471\)
\(a_{56}=-1.112167977\) \(a_{57}=+0.985614985\) \(a_{58}=+0.127355112\) \(a_{59}=+1.728067538\) \(a_{60}=-0.274104500\)
\(a_{61}=-0.502902395\) \(a_{62}=+0.146989970\) \(a_{63}=-0.552181641\) \(a_{64}=-0.308373851\) \(a_{65}=-0.250656283\)
\(a_{66}=+0.128649151\) \(a_{67}=+0.767663233\) \(a_{68}=+0.460253963\) \(a_{69}=-0.658628875\) \(a_{70}=+0.323857052\)
\(a_{71}=-0.213978306\) \(a_{72}=+0.223792699\) \(a_{73}=+0.621371190\) \(a_{74}=-0.351455266\) \(a_{75}=-0.405922508\)
\(a_{76}=-1.487386476\) \(a_{77}=+1.028825027\) \(a_{78}=+0.095285392\) \(a_{79}=+0.100062500\) \(a_{80}=+0.343507482\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.687402661\) \(a_{83}=+0.655506567\) \(a_{84}=+0.833294458\) \(a_{85}=-0.287847541\)
\(a_{86}=-0.319192779\) \(a_{87}=-0.204939894\) \(a_{88}=-0.416970634\) \(a_{89}=-1.184099498\) \(a_{90}=-0.065167174\)
\(a_{91}=+0.762010442\) \(a_{92}=+0.993933428\) \(a_{93}=-0.236536313\) \(a_{94}=-0.104848073\) \(a_{95}=+0.930226731\)
\(a_{96}=-0.518202510\) \(a_{97}=+0.526457277\) \(a_{98}=-0.625764414\) \(a_{99}=-0.207022261\) \(a_{100}=+0.612575557\)

Showing 100 of 1228 available coefficients

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