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: \( 23.9170819774 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.567845570\) \(a_{3}=+0.577350269\) \(a_{4}=-0.677551408\) \(a_{5}=+1.444046106\)
\(a_{6}=-0.327845793\) \(a_{7}=+1.036390284\) \(a_{8}=+0.952590136\) \(a_{9}=+0.333333333\) \(a_{10}=-0.819995185\)
\(a_{11}=+0.116046452\) \(a_{12}=-0.391184488\) \(a_{13}=+1.184733397\) \(a_{14}=-0.588509632\) \(a_{15}=+0.833720408\)
\(a_{16}=+0.136627319\) \(a_{17}=+0.693091621\) \(a_{18}=-0.189281857\) \(a_{19}=-1.418462652\) \(a_{20}=-0.978415473\)
\(a_{21}=+0.598360209\) \(a_{22}=-0.065896464\) \(a_{23}=-0.774170691\) \(a_{24}=+0.549978172\) \(a_{25}=+1.085269157\)
\(a_{26}=-0.672745612\) \(a_{27}=+0.192450090\) \(a_{28}=-0.702207696\) \(a_{29}=-1.515631788\) \(a_{30}=-0.473424441\)
\(a_{31}=+1.438558254\) \(a_{32}=-1.030173354\) \(a_{33}=+0.066999450\) \(a_{34}=-0.393569007\) \(a_{35}=+1.496595354\)
\(a_{36}=-0.225850469\) \(a_{37}=+0.842199780\) \(a_{38}=+0.805467734\) \(a_{39}=+0.684006146\) \(a_{40}=+1.375584077\)
\(a_{41}=+0.264920566\) \(a_{42}=-0.339776194\) \(a_{43}=+1.009857608\) \(a_{44}=-0.078627437\) \(a_{45}=+0.481348702\)
\(a_{46}=+0.439609398\) \(a_{47}=+1.130624349\) \(a_{48}=+0.078881819\) \(a_{49}=+0.074104820\) \(a_{50}=-0.616265283\)
\(a_{51}=+0.400156634\) \(a_{52}=-0.802717781\) \(a_{53}=+0.831731902\) \(a_{54}=-0.109281931\) \(a_{55}=+0.167576427\)
\(a_{56}=+0.987255162\) \(a_{57}=-0.818949794\) \(a_{58}=+0.860644797\) \(a_{59}=-0.081630987\) \(a_{60}=-0.564888436\)
\(a_{61}=-0.614691566\) \(a_{62}=-0.816878933\) \(a_{63}=+0.345463428\) \(a_{64}=+0.448352057\) \(a_{65}=+1.710809648\)
\(a_{66}=-0.038045341\) \(a_{67}=-0.408919279\) \(a_{68}=-0.469605204\) \(a_{69}=-0.446967657\) \(a_{70}=-0.849835042\)
\(a_{71}=+1.470499699\) \(a_{72}=+0.317530045\) \(a_{73}=-1.385187467\) \(a_{74}=-0.478239414\) \(a_{75}=+0.626580440\)
\(a_{76}=+0.961081367\) \(a_{77}=+0.120269415\) \(a_{78}=-0.388409860\) \(a_{79}=+0.002898770\) \(a_{80}=+0.197296148\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.150433970\) \(a_{83}=-0.517276412\) \(a_{84}=-0.405419802\) \(a_{85}=+1.000856256\)
\(a_{86}=-0.573443170\) \(a_{87}=-0.875050421\) \(a_{88}=+0.110544705\) \(a_{89}=+0.607053150\) \(a_{90}=-0.273331728\)
\(a_{91}=+1.227846181\) \(a_{92}=+0.524540442\) \(a_{93}=+0.830551995\) \(a_{94}=-0.642020028\) \(a_{95}=-2.048325470\)
\(a_{96}=-0.594770863\) \(a_{97}=+1.164227596\) \(a_{98}=-0.042080094\) \(a_{99}=+0.038682151\) \(a_{100}=-0.735325645\)

Showing 100 of 1228 available coefficients

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