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: \( 29.9680209354 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.317823174\) \(a_{3}=-0.577350269\) \(a_{4}=+0.736657918\) \(a_{5}=+1.719026588\)
\(a_{6}=-0.760845564\) \(a_{7}=-0.779919184\) \(a_{8}=-0.347038299\) \(a_{9}=+0.333333333\) \(a_{10}=+2.265373075\)
\(a_{11}=-0.852723063\) \(a_{12}=-0.425309647\) \(a_{13}=-0.017148164\) \(a_{14}=-1.027795575\) \(a_{15}=-0.992480464\)
\(a_{16}=-1.193993030\) \(a_{17}=+0.303846627\) \(a_{18}=+0.439274391\) \(a_{19}=-1.625818475\) \(a_{20}=+1.266334547\)
\(a_{21}=+0.450286551\) \(a_{22}=-1.123738213\) \(a_{23}=+0.971938062\) \(a_{24}=+0.200362655\) \(a_{25}=+1.955052412\)
\(a_{26}=-0.022598249\) \(a_{27}=-0.192450090\) \(a_{28}=-0.574533642\) \(a_{29}=+0.013319293\) \(a_{30}=-1.307913755\)
\(a_{31}=-1.891627525\) \(a_{32}=-1.226433386\) \(a_{33}=+0.492319890\) \(a_{34}=+0.400416126\) \(a_{35}=-1.340701815\)
\(a_{36}=+0.245552639\) \(a_{37}=+1.173398808\) \(a_{38}=-2.142541263\) \(a_{39}=+0.009900497\) \(a_{40}=-0.596568063\)
\(a_{41}=-0.530083782\) \(a_{42}=+0.593398052\) \(a_{43}=-0.892475946\) \(a_{44}=-0.628165196\) \(a_{45}=+0.573008863\)
\(a_{46}=+1.280842501\) \(a_{47}=-0.710741665\) \(a_{48}=+0.689352197\) \(a_{49}=-0.391726066\) \(a_{50}=+2.576413375\)
\(a_{51}=-0.175425932\) \(a_{52}=-0.012632331\) \(a_{53}=-0.402243739\) \(a_{54}=-0.253615188\) \(a_{55}=-1.465853618\)
\(a_{56}=+0.270661827\) \(a_{57}=+0.938666734\) \(a_{58}=+0.017552473\) \(a_{59}=-1.307938061\) \(a_{60}=-0.731118592\)
\(a_{61}=-0.358950295\) \(a_{62}=-2.492830589\) \(a_{63}=-0.259973061\) \(a_{64}=-0.422229307\) \(a_{65}=-0.029478151\)
\(a_{66}=+0.648790560\) \(a_{67}=-0.996094323\) \(a_{68}=+0.223831023\) \(a_{69}=-0.561148701\) \(a_{70}=-1.766807921\)
\(a_{71}=-0.846971541\) \(a_{72}=-0.115679433\) \(a_{73}=+0.188570887\) \(a_{74}=+1.546332141\) \(a_{75}=-1.128750036\)
\(a_{76}=-1.197672052\) \(a_{77}=+0.665055076\) \(a_{78}=+0.013047105\) \(a_{79}=+1.433982561\) \(a_{80}=-2.052505765\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.698556691\) \(a_{83}=+0.529814890\) \(a_{84}=+0.331707153\) \(a_{85}=+0.522320430\)
\(a_{86}=-1.176125484\) \(a_{87}=-0.007689897\) \(a_{88}=+0.295927561\) \(a_{89}=-0.566605074\) \(a_{90}=+0.755124358\)
\(a_{91}=+0.013374182\) \(a_{92}=+0.715985868\) \(a_{93}=+1.092131661\) \(a_{94}=-0.936631837\) \(a_{95}=-2.794825187\)
\(a_{96}=+0.708081645\) \(a_{97}=+1.089494306\) \(a_{98}=-0.516225687\) \(a_{99}=-0.284241021\) \(a_{100}=+1.440204839\)

Showing 100 of 1228 available coefficients

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