Properties

Level $87$
Weight $0$
Character 87.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 87 = 3 \cdot 29 \)
Weight: \( 0 \)
Character: 87.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.25756312047 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.812961100\) \(a_{3}=-0.577350269\) \(a_{4}=+2.286827949\) \(a_{5}=+0.653734040\)
\(a_{6}=-1.046713579\) \(a_{7}=+1.375356405\) \(a_{8}=+2.332969014\) \(a_{9}=+0.333333333\) \(a_{10}=+1.185194385\)
\(a_{11}=-1.284213584\) \(a_{12}=-1.320300732\) \(a_{13}=-0.315523269\) \(a_{14}=+2.493467660\) \(a_{15}=-0.377433524\)
\(a_{16}=+1.942754120\) \(a_{17}=-0.108545705\) \(a_{18}=+0.604320367\) \(a_{19}=-1.775783866\) \(a_{20}=+1.494977275\)
\(a_{21}=-0.794062390\) \(a_{22}=-2.328229271\) \(a_{23}=+0.612027646\) \(a_{24}=-1.346940288\) \(a_{25}=-0.572631804\)
\(a_{26}=-0.572031412\) \(a_{27}=-0.192450090\) \(a_{28}=+3.145203466\) \(a_{29}=+0.185695338\) \(a_{30}=-0.684272297\)
\(a_{31}=+1.739070336\) \(a_{32}=+1.189168632\) \(a_{33}=+0.741441058\) \(a_{34}=-0.196789140\) \(a_{35}=+0.899117299\)
\(a_{36}=+0.762275983\) \(a_{37}=-1.187471402\) \(a_{38}=-3.219427070\) \(a_{39}=+0.182167444\) \(a_{40}=+1.525141260\)
\(a_{41}=+0.711237967\) \(a_{42}=-1.439604225\) \(a_{43}=-0.354490886\) \(a_{44}=-2.936775516\) \(a_{45}=+0.217911347\)
\(a_{46}=+1.109582314\) \(a_{47}=+0.042223668\) \(a_{48}=-1.121649614\) \(a_{49}=+0.891605240\) \(a_{50}=-1.038159186\)
\(a_{51}=+0.062668892\) \(a_{52}=-0.721547430\) \(a_{53}=-1.158178715\) \(a_{54}=-0.348904526\) \(a_{55}=-0.839534135\)
\(a_{56}=+3.208663875\) \(a_{57}=+1.025249293\) \(a_{58}=+0.336658425\) \(a_{59}=+1.639326585\) \(a_{60}=-0.863125532\)
\(a_{61}=-0.570215580\) \(a_{62}=+3.152866869\) \(a_{63}=+0.458452135\) \(a_{64}=+0.213162350\) \(a_{65}=-0.206268301\)
\(a_{66}=+1.344203796\) \(a_{67}=-0.582612744\) \(a_{68}=-0.248225352\) \(a_{69}=-0.353354326\) \(a_{70}=+1.630064688\)
\(a_{71}=+1.509449781\) \(a_{72}=+0.777656338\) \(a_{73}=+1.514450145\) \(a_{74}=-2.152839459\) \(a_{75}=+0.330609126\)
\(a_{76}=-4.060912176\) \(a_{77}=-1.766251377\) \(a_{78}=+0.330262490\) \(a_{79}=-0.950834829\) \(a_{80}=+1.270044500\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.289446768\) \(a_{83}=+1.708873373\) \(a_{84}=-1.815884068\) \(a_{85}=-0.070960022\)
\(a_{86}=-0.642678187\) \(a_{87}=-0.107211253\) \(a_{88}=-2.996030498\) \(a_{89}=+0.631459547\) \(a_{90}=+0.395064795\)
\(a_{91}=-0.433956949\) \(a_{92}=+1.399601926\) \(a_{93}=-1.004052727\) \(a_{94}=+0.076549867\) \(a_{95}=-1.160890362\)
\(a_{96}=-0.686566830\) \(a_{97}=-1.174806106\) \(a_{98}=+1.616445616\) \(a_{99}=-0.428071195\) \(a_{100}=-1.309510415\)

Showing 100 of 726 available coefficients

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