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: \( 27.2434546598 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.081105839\) \(a_{3}=-0.577350269\) \(a_{4}=-0.993421843\) \(a_{5}=-1.141097836\)
\(a_{6}=-0.046826478\) \(a_{7}=-0.058147373\) \(a_{8}=-0.161678151\) \(a_{9}=+0.333333333\) \(a_{10}=-0.092549697\)
\(a_{11}=+1.325916157\) \(a_{12}=+0.573552368\) \(a_{13}=+0.625847758\) \(a_{14}=-0.004716091\) \(a_{15}=+0.658813143\)
\(a_{16}=+0.980308801\) \(a_{17}=-0.128775226\) \(a_{18}=+0.027035280\) \(a_{19}=+0.202633974\) \(a_{20}=+1.133591515\)
\(a_{21}=+0.033571401\) \(a_{22}=+0.107539542\) \(a_{23}=-1.073614722\) \(a_{24}=+0.093344924\) \(a_{25}=+0.302104271\)
\(a_{26}=+0.050759907\) \(a_{27}=-0.192450090\) \(a_{28}=+0.057764870\) \(a_{29}=+1.337990863\) \(a_{30}=+0.053433593\)
\(a_{31}=-1.812825223\) \(a_{32}=+0.241186918\) \(a_{33}=-0.765518050\) \(a_{34}=-0.010444423\) \(a_{35}=+0.066351841\)
\(a_{36}=-0.331140614\) \(a_{37}=+1.586262680\) \(a_{38}=+0.016434798\) \(a_{39}=-0.361333371\) \(a_{40}=+0.184490588\)
\(a_{41}=+1.391286859\) \(a_{42}=+0.002722837\) \(a_{43}=+1.128209676\) \(a_{44}=-1.317194072\) \(a_{45}=-0.380365945\)
\(a_{46}=-0.087076423\) \(a_{47}=-0.863868645\) \(a_{48}=-0.565981550\) \(a_{49}=-0.996618883\) \(a_{50}=+0.024502420\)
\(a_{51}=+0.074348411\) \(a_{52}=-0.621730833\) \(a_{53}=-1.762925084\) \(a_{54}=-0.015608826\) \(a_{55}=-1.513000057\)
\(a_{56}=+0.009401160\) \(a_{57}=-0.116990780\) \(a_{58}=+0.108518871\) \(a_{59}=-0.558318849\) \(a_{60}=-0.654479366\)
\(a_{61}=+0.546605063\) \(a_{62}=-0.147030710\) \(a_{63}=-0.019382458\) \(a_{64}=-0.960747134\) \(a_{65}=-0.714153522\)
\(a_{66}=-0.062087984\) \(a_{67}=+0.211975364\) \(a_{68}=+0.127928122\) \(a_{69}=+0.619851749\) \(a_{70}=+0.005381522\)
\(a_{71}=+0.450618784\) \(a_{72}=-0.053892717\) \(a_{73}=-1.300877088\) \(a_{74}=+0.128655165\) \(a_{75}=-0.174419982\)
\(a_{76}=-0.201301016\) \(a_{77}=-0.077098541\) \(a_{78}=-0.029306246\) \(a_{79}=+1.733213426\) \(a_{80}=-1.118628251\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.112841488\) \(a_{83}=+0.147862271\) \(a_{84}=-0.033350563\) \(a_{85}=+0.146945131\)
\(a_{86}=+0.091504392\) \(a_{87}=-0.772489385\) \(a_{88}=-0.214371672\) \(a_{89}=-0.517572078\) \(a_{90}=-0.030849899\)
\(a_{91}=-0.036391403\) \(a_{92}=+1.066552316\) \(a_{93}=+1.046635130\) \(a_{94}=-0.070064791\) \(a_{95}=-0.231225190\)
\(a_{96}=-0.139249332\) \(a_{97}=-0.926264665\) \(a_{98}=-0.080831610\) \(a_{99}=+0.441972052\) \(a_{100}=-0.300116982\)

Showing 100 of 1228 available coefficients

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