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: \( 15.1595355562 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.952072561\) \(a_{3}=+0.577350269\) \(a_{4}=-0.093557838\) \(a_{5}=-0.269849115\)
\(a_{6}=+0.549679350\) \(a_{7}=-1.667012773\) \(a_{8}=-1.041146412\) \(a_{9}=+0.333333333\) \(a_{10}=-0.256915938\)
\(a_{11}=+0.566424365\) \(a_{12}=-0.054015643\) \(a_{13}=-0.332388922\) \(a_{14}=-1.587117121\) \(a_{15}=-0.155797459\)
\(a_{16}=-0.897689093\) \(a_{17}=-0.716524671\) \(a_{18}=+0.317357520\) \(a_{19}=-1.160041314\) \(a_{20}=+0.025246500\)
\(a_{21}=-0.962450273\) \(a_{22}=+0.539277096\) \(a_{23}=+1.098873781\) \(a_{24}=-0.601106161\) \(a_{25}=-0.927181455\)
\(a_{26}=-0.316458372\) \(a_{27}=+0.192450090\) \(a_{28}=+0.155962111\) \(a_{29}=+1.393425571\) \(a_{30}=-0.148330486\)
\(a_{31}=-1.433116663\) \(a_{32}=+0.186481258\) \(a_{33}=+0.327025260\) \(a_{34}=-0.682183479\) \(a_{35}=+0.449841922\)
\(a_{36}=-0.031185946\) \(a_{37}=+1.425717929\) \(a_{38}=-1.104443505\) \(a_{39}=-0.191904833\) \(a_{40}=+0.280952438\)
\(a_{41}=+0.150195319\) \(a_{42}=-0.916322497\) \(a_{43}=+0.289875134\) \(a_{44}=-0.052993439\) \(a_{45}=-0.089949705\)
\(a_{46}=+1.046207575\) \(a_{47}=-0.485518710\) \(a_{48}=-0.518281039\) \(a_{49}=+1.778931586\) \(a_{50}=-0.882744023\)
\(a_{51}=-0.413685712\) \(a_{52}=+0.031097589\) \(a_{53}=-1.314968488\) \(a_{54}=+0.183226450\) \(a_{55}=-0.152849114\)
\(a_{56}=+1.735604367\) \(a_{57}=-0.669750165\) \(a_{58}=+1.326642253\) \(a_{59}=-0.001820070\) \(a_{60}=+0.014576073\)
\(a_{61}=-0.854078196\) \(a_{62}=-1.364431052\) \(a_{63}=-0.555670924\) \(a_{64}=+1.075232782\) \(a_{65}=+0.089694856\)
\(a_{66}=+0.311351777\) \(a_{67}=-0.075379734\) \(a_{68}=+0.067036499\) \(a_{69}=+0.634435073\) \(a_{70}=+0.428282151\)
\(a_{71}=-0.557409353\) \(a_{72}=-0.347048804\) \(a_{73}=-0.706385751\) \(a_{74}=+1.357386920\) \(a_{75}=-0.535308463\)
\(a_{76}=+0.108530957\) \(a_{77}=-0.944236652\) \(a_{78}=-0.182707326\) \(a_{79}=+0.203371947\) \(a_{80}=+0.242240608\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.142996842\) \(a_{83}=+0.284889889\) \(a_{84}=+0.090044767\) \(a_{85}=+0.193353549\)
\(a_{86}=+0.275982161\) \(a_{87}=+0.804494629\) \(a_{88}=-0.589730695\) \(a_{89}=-1.456159521\) \(a_{90}=-0.085638646\)
\(a_{91}=+0.554096578\) \(a_{92}=-0.102808255\) \(a_{93}=-0.827410291\) \(a_{94}=-0.462249041\) \(a_{95}=+0.313036122\)
\(a_{96}=+0.107665004\) \(a_{97}=+0.704311663\) \(a_{98}=+1.693671952\) \(a_{99}=+0.188808122\) \(a_{100}=+0.086745092\)

Showing 100 of 1228 available coefficients

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