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: \( 21.3531715323 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.398537401\) \(a_{3}=+0.577350269\) \(a_{4}=-0.841167940\) \(a_{5}=-0.920971092\)
\(a_{6}=+0.230095676\) \(a_{7}=-1.541605303\) \(a_{8}=-0.733774286\) \(a_{9}=+0.333333333\) \(a_{10}=-0.367041426\)
\(a_{11}=+0.580355881\) \(a_{12}=-0.485648536\) \(a_{13}=+1.462891279\) \(a_{14}=-0.614387371\) \(a_{15}=-0.531722908\)
\(a_{16}=+0.548731442\) \(a_{17}=+1.192957931\) \(a_{18}=+0.132845800\) \(a_{19}=-0.085371141\) \(a_{20}=+0.774691356\)
\(a_{21}=-0.890046237\) \(a_{22}=+0.231293525\) \(a_{23}=-1.177281686\) \(a_{24}=-0.423644782\) \(a_{25}=-0.151812247\)
\(a_{26}=+0.583016889\) \(a_{27}=+0.192450090\) \(a_{28}=+1.296748956\) \(a_{29}=+0.157751690\) \(a_{30}=-0.211911466\)
\(a_{31}=+1.373861379\) \(a_{32}=+0.952464289\) \(a_{33}=+0.335068624\) \(a_{34}=+0.475438354\) \(a_{35}=+1.419773920\)
\(a_{36}=-0.280389313\) \(a_{37}=-0.465953636\) \(a_{38}=-0.034023593\) \(a_{39}=+0.844600674\) \(a_{40}=+0.675784906\)
\(a_{41}=+0.029929270\) \(a_{42}=-0.354716714\) \(a_{43}=+1.016509043\) \(a_{44}=-0.488176761\) \(a_{45}=-0.306990364\)
\(a_{46}=-0.469190784\) \(a_{47}=-0.342114083\) \(a_{48}=+0.316810246\) \(a_{49}=+1.376546910\) \(a_{50}=-0.060502859\)
\(a_{51}=+0.688754583\) \(a_{52}=-1.230537243\) \(a_{53}=-0.565288182\) \(a_{54}=+0.076698559\) \(a_{55}=-0.534490990\)
\(a_{56}=+1.131190331\) \(a_{57}=-0.049289051\) \(a_{58}=+0.062869949\) \(a_{59}=-0.670858725\) \(a_{60}=+0.447268263\)
\(a_{61}=+0.475720438\) \(a_{62}=+0.547535144\) \(a_{63}=-0.513868434\) \(a_{64}=-0.169138800\) \(a_{65}=-1.347280579\)
\(a_{66}=+0.133537379\) \(a_{67}=+1.523991518\) \(a_{68}=-1.003477965\) \(a_{69}=-0.679703898\) \(a_{70}=+0.565833009\)
\(a_{71}=+1.643185711\) \(a_{72}=-0.244591429\) \(a_{73}=-0.419753534\) \(a_{74}=-0.185699951\) \(a_{75}=-0.087648842\)
\(a_{76}=+0.071811467\) \(a_{77}=-0.894679704\) \(a_{78}=+0.336604958\) \(a_{79}=-0.062494341\) \(a_{80}=-0.505365796\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.011927934\) \(a_{83}=+1.323072461\) \(a_{84}=+0.748678359\) \(a_{85}=-1.098679769\)
\(a_{86}=+0.405116872\) \(a_{87}=+0.091077981\) \(a_{88}=-0.425850222\) \(a_{89}=+0.052060224\) \(a_{90}=-0.122347142\)
\(a_{91}=-2.255200953\) \(a_{92}=+0.990291610\) \(a_{93}=+0.793199237\) \(a_{94}=-0.136345258\) \(a_{95}=+0.078624353\)
\(a_{96}=+0.549905514\) \(a_{97}=-0.265952050\) \(a_{98}=+0.548605428\) \(a_{99}=+0.193451960\) \(a_{100}=+0.127699595\)

Showing 100 of 1228 available coefficients

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