Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 24.1123527298 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.712436870\) \(a_{3}=+0.881068053\) \(a_{4}=+1.932440035\) \(a_{5}=-0.355367733\)
\(a_{6}=+1.508773419\) \(a_{7}=+1.315449087\) \(a_{8}=+1.596744694\) \(a_{9}=-0.223719086\) \(a_{10}=-0.608544809\)
\(a_{11}=-0.533283346\) \(a_{12}=+1.702611179\) \(a_{13}=+0.053309768\) \(a_{14}=+2.252623496\) \(a_{15}=-0.313103157\)
\(a_{16}=+0.801884453\) \(a_{17}=+0.452635404\) \(a_{18}=-0.383104811\) \(a_{19}=+0.552333945\) \(a_{20}=-0.686726835\)
\(a_{21}=+1.159000166\) \(a_{22}=-0.913214065\) \(a_{23}=-0.372791909\) \(a_{24}=+1.406840739\) \(a_{25}=-0.873713774\)
\(a_{26}=+0.091289610\) \(a_{27}=-1.078179792\) \(a_{28}=+2.542026478\) \(a_{29}=-1.699927190\) \(a_{30}=-0.536169390\)
\(a_{31}=+1.148139475\) \(a_{32}=-0.223568192\) \(a_{33}=-0.469858920\) \(a_{34}=+0.775109555\) \(a_{35}=-0.467468160\)
\(a_{36}=-0.432323718\) \(a_{37}=+0.060729296\) \(a_{38}=+0.945837012\) \(a_{39}=+0.046969532\) \(a_{40}=-0.567431543\)
\(a_{41}=-1.673302329\) \(a_{42}=+1.984714617\) \(a_{43}=+0.644830744\) \(a_{44}=-1.030538089\) \(a_{45}=+0.079502544\)
\(a_{46}=-0.638382609\) \(a_{47}=+0.124821626\) \(a_{48}=+0.706514774\) \(a_{49}=+0.730406300\) \(a_{50}=-1.496179681\)
\(a_{51}=+0.398802594\) \(a_{52}=+0.103017927\) \(a_{53}=+0.767439588\) \(a_{54}=-1.846314830\) \(a_{55}=+0.189511694\)
\(a_{56}=+2.100436350\) \(a_{57}=+0.486643794\) \(a_{58}=-2.911017997\) \(a_{59}=+1.042780213\) \(a_{60}=-0.605053068\)
\(a_{61}=+0.103827334\) \(a_{62}=+1.966116363\) \(a_{63}=-0.294291067\) \(a_{64}=-1.184730868\) \(a_{65}=-0.018944571\)
\(a_{66}=-0.804603738\) \(a_{67}=+0.787565561\) \(a_{68}=+0.874690776\) \(a_{69}=-0.328455041\) \(a_{70}=-0.800509713\)
\(a_{71}=+1.078491496\) \(a_{72}=-0.357222263\) \(a_{73}=-0.374099232\) \(a_{74}=+0.103995086\) \(a_{75}=-0.769801294\)
\(a_{76}=+1.067352228\) \(a_{77}=-0.701507091\) \(a_{78}=+0.080432359\) \(a_{79}=+1.824745925\) \(a_{80}=-0.284963860\)
\(a_{81}=-0.726230685\) \(a_{82}=-2.865424603\) \(a_{83}=+0.883136108\) \(a_{84}=+2.239698321\) \(a_{85}=-0.160852018\)
\(a_{86}=+1.104231942\) \(a_{87}=-1.497751540\) \(a_{88}=-0.851517354\) \(a_{89}=+0.435824250\) \(a_{90}=+0.136143088\)
\(a_{91}=+0.070126284\) \(a_{92}=-0.720398009\) \(a_{93}=+1.011589013\) \(a_{94}=+0.213749154\) \(a_{95}=-0.196281662\)
\(a_{96}=-0.196978791\) \(a_{97}=-0.480469344\) \(a_{98}=+1.250774676\) \(a_{99}=+0.119305662\) \(a_{100}=-1.688399474\)

Showing 100 of 5000 available coefficients

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