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: \( 2.80239725348 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.136943044\) \(a_{3}=-0.577350269\) \(a_{4}=-0.981246603\) \(a_{5}=-1.393547121\)
\(a_{6}=+0.079064104\) \(a_{7}=+0.803037832\) \(a_{8}=+0.271317942\) \(a_{9}=+0.333333333\) \(a_{10}=+0.190836585\)
\(a_{11}=-0.023576217\) \(a_{12}=+0.566522990\) \(a_{13}=-1.184528675\) \(a_{14}=-0.109970446\) \(a_{15}=+0.804564805\)
\(a_{16}=+0.944091498\) \(a_{17}=+1.301311831\) \(a_{18}=-0.045647681\) \(a_{19}=-0.512700223\) \(a_{20}=+1.367413378\)
\(a_{21}=-0.463634108\) \(a_{22}=+0.003228599\) \(a_{23}=-0.033082563\) \(a_{24}=-0.156645487\) \(a_{25}=+0.941973578\)
\(a_{26}=+0.162212963\) \(a_{27}=-0.192450090\) \(a_{28}=-0.787978144\) \(a_{29}=+0.185695338\) \(a_{30}=-0.110179554\)
\(a_{31}=-0.783747118\) \(a_{32}=-0.400604706\) \(a_{33}=+0.013611735\) \(a_{34}=-0.178205604\) \(a_{35}=-1.119071059\)
\(a_{36}=-0.327082201\) \(a_{37}=+0.794759103\) \(a_{38}=+0.070210729\) \(a_{39}=+0.683887949\) \(a_{40}=-0.378094336\)
\(a_{41}=+1.608939525\) \(a_{42}=+0.063491466\) \(a_{43}=-0.633892314\) \(a_{44}=+0.023134083\) \(a_{45}=-0.464515707\)
\(a_{46}=+0.004530427\) \(a_{47}=+1.261836033\) \(a_{48}=-0.545071480\) \(a_{49}=-0.355130241\) \(a_{50}=-0.128996730\)
\(a_{51}=-0.751312736\) \(a_{52}=+1.162314738\) \(a_{53}=-0.570233858\) \(a_{54}=+0.026354701\) \(a_{55}=+0.032854570\)
\(a_{56}=+0.217878572\) \(a_{57}=+0.296007612\) \(a_{58}=-0.025429685\) \(a_{59}=+1.257190022\) \(a_{60}=-0.789476482\)
\(a_{61}=+1.568561278\) \(a_{62}=+0.107328716\) \(a_{63}=+0.267679277\) \(a_{64}=-0.889231470\) \(a_{65}=+1.650696524\)
\(a_{66}=-0.001864032\) \(a_{67}=-1.233809344\) \(a_{68}=-1.276907813\) \(a_{69}=+0.019100227\) \(a_{70}=+0.153248998\)
\(a_{71}=+1.303902369\) \(a_{72}=+0.090439314\) \(a_{73}=+0.661561165\) \(a_{74}=-0.108836731\) \(a_{75}=-0.543848699\)
\(a_{76}=+0.503085352\) \(a_{77}=-0.018932594\) \(a_{78}=-0.093653698\) \(a_{79}=+1.353493543\) \(a_{80}=-1.315635988\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.220333077\) \(a_{83}=-0.100909817\) \(a_{84}=+0.454939394\) \(a_{85}=-1.813439356\)
\(a_{86}=+0.086807143\) \(a_{87}=-0.107211253\) \(a_{88}=-0.006396651\) \(a_{89}=-1.488815333\) \(a_{90}=+0.063612195\)
\(a_{91}=-0.951221339\) \(a_{92}=+0.032462152\) \(a_{93}=+0.452496609\) \(a_{94}=-0.172799668\) \(a_{95}=+0.714471920\)
\(a_{96}=+0.231289235\) \(a_{97}=-0.395979359\) \(a_{98}=+0.048632616\) \(a_{99}=-0.007858739\) \(a_{100}=-0.924308373\)

Showing 100 of 760 available coefficients

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