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: \( 30.0509363683 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.913047934\) \(a_{3}=-0.577350269\) \(a_{4}=-0.166343470\) \(a_{5}=-0.843297339\)
\(a_{6}=-0.527148471\) \(a_{7}=-0.099836813\) \(a_{8}=-1.064927496\) \(a_{9}=+0.333333333\) \(a_{10}=-0.769970894\)
\(a_{11}=-0.234188096\) \(a_{12}=+0.096038447\) \(a_{13}=-1.673484357\) \(a_{14}=-0.091155796\) \(a_{15}=+0.486877946\)
\(a_{16}=-0.805986381\) \(a_{17}=+0.242148258\) \(a_{18}=+0.304349311\) \(a_{19}=-0.991418407\) \(a_{20}=+0.140277005\)
\(a_{21}=+0.057640811\) \(a_{22}=-0.213824957\) \(a_{23}=-1.152799512\) \(a_{24}=+0.614836176\) \(a_{25}=-0.288849598\)
\(a_{26}=-1.527971435\) \(a_{27}=-0.192450090\) \(a_{28}=+0.016607202\) \(a_{29}=+1.590096515\) \(a_{30}=+0.444542903\)
\(a_{31}=+1.127488817\) \(a_{32}=+0.329023296\) \(a_{33}=+0.135208560\) \(a_{34}=+0.221092967\) \(a_{35}=+0.084192119\)
\(a_{36}=-0.055447823\) \(a_{37}=+0.405158882\) \(a_{38}=-0.905212529\) \(a_{39}=+0.966186644\) \(a_{40}=+0.898050524\)
\(a_{41}=+0.334194690\) \(a_{42}=+0.052628823\) \(a_{43}=+0.886822442\) \(a_{44}=+0.038955660\) \(a_{45}=-0.281099113\)
\(a_{46}=-1.052561213\) \(a_{47}=-0.483204310\) \(a_{48}=+0.465336454\) \(a_{49}=-0.990032611\) \(a_{50}=-0.263733529\)
\(a_{51}=-0.139804362\) \(a_{52}=+0.278373194\) \(a_{53}=-1.024106201\) \(a_{54}=-0.175716157\) \(a_{55}=+0.197490198\)
\(a_{56}=+0.106318968\) \(a_{57}=+0.572395684\) \(a_{58}=+1.451834339\) \(a_{59}=+1.762743885\) \(a_{60}=-0.080988967\)
\(a_{61}=-1.145866348\) \(a_{62}=+1.029451335\) \(a_{63}=-0.033278938\) \(a_{64}=+1.106400421\) \(a_{65}=+1.411244906\)
\(a_{66}=+0.123451897\) \(a_{67}=+1.493348883\) \(a_{68}=-0.040279781\) \(a_{69}=+0.665569109\) \(a_{70}=+0.076871440\)
\(a_{71}=-0.762645593\) \(a_{72}=-0.354975832\) \(a_{73}=+1.481648548\) \(a_{74}=+0.369929480\) \(a_{75}=+0.166767393\)
\(a_{76}=+0.164915978\) \(a_{77}=+0.023380593\) \(a_{78}=+0.882174720\) \(a_{79}=-1.002876689\) \(a_{80}=+0.679686170\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.305135771\) \(a_{83}=-0.788649538\) \(a_{84}=-0.009588173\) \(a_{85}=-0.204202982\)
\(a_{86}=+0.809711398\) \(a_{87}=-0.918042651\) \(a_{88}=+0.249393342\) \(a_{89}=+1.176853306\) \(a_{90}=-0.256656965\)
\(a_{91}=+0.167075345\) \(a_{92}=+0.191760671\) \(a_{93}=-0.650955972\) \(a_{94}=-0.441188697\) \(a_{95}=+0.836060505\)
\(a_{96}=-0.189961688\) \(a_{97}=-0.299031209\) \(a_{98}=-0.903947230\) \(a_{99}=-0.078062699\) \(a_{100}=+0.048048244\)

Showing 100 of 1228 available coefficients

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