Properties

Level $87$
Weight $0$
Character 87.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 87 = 3 \cdot 29 \)
Weight: \( 0 \)
Character: 87.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.06508325829 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.113529946\) \(a_{3}=-0.577350269\) \(a_{4}=-0.987110951\) \(a_{5}=+0.811036659\)
\(a_{6}=-0.065546545\) \(a_{7}=+0.453609871\) \(a_{8}=-0.225596600\) \(a_{9}=+0.333333333\) \(a_{10}=+0.092076949\)
\(a_{11}=-0.823364461\) \(a_{12}=+0.569908773\) \(a_{13}=+0.578391222\) \(a_{14}=+0.051498304\) \(a_{15}=-0.468252233\)
\(a_{16}=+0.961498981\) \(a_{17}=+0.252424377\) \(a_{18}=+0.037843315\) \(a_{19}=+0.836629669\) \(a_{20}=-0.800583168\)
\(a_{21}=-0.261891781\) \(a_{22}=-0.093476523\) \(a_{23}=+1.384498636\) \(a_{24}=+0.130248258\) \(a_{25}=-0.342219538\)
\(a_{26}=+0.065664724\) \(a_{27}=-0.192450090\) \(a_{28}=-0.447763271\) \(a_{29}=-0.185695338\) \(a_{30}=-0.053160651\)
\(a_{31}=+0.885560551\) \(a_{32}=+0.334755528\) \(a_{33}=+0.475369693\) \(a_{34}=+0.028657726\) \(a_{35}=+0.367894234\)
\(a_{36}=-0.329036984\) \(a_{37}=+0.674341902\) \(a_{38}=+0.094982522\) \(a_{39}=-0.333934327\) \(a_{40}=-0.182967113\)
\(a_{41}=+1.358337172\) \(a_{42}=-0.029732560\) \(a_{43}=+0.376525374\) \(a_{44}=+0.812752076\) \(a_{45}=+0.270345553\)
\(a_{46}=+0.157182056\) \(a_{47}=+0.245866866\) \(a_{48}=-0.555121696\) \(a_{49}=-0.794238085\) \(a_{50}=-0.038852166\)
\(a_{51}=-0.145737282\) \(a_{52}=-0.570936309\) \(a_{53}=-0.593822629\) \(a_{54}=-0.021848848\) \(a_{55}=-0.667778761\)
\(a_{56}=-0.102332845\) \(a_{57}=-0.483028365\) \(a_{58}=-0.021081982\) \(a_{59}=+0.887664413\) \(a_{60}=+0.462216908\)
\(a_{61}=-0.507403116\) \(a_{62}=+0.100537642\) \(a_{63}=+0.151203290\) \(a_{64}=-0.923494204\) \(a_{65}=+0.469096484\)
\(a_{66}=+0.053968696\) \(a_{67}=-0.750012869\) \(a_{68}=-0.249170867\) \(a_{69}=-0.799340660\) \(a_{70}=+0.041767013\)
\(a_{71}=+1.353965948\) \(a_{72}=-0.075198867\) \(a_{73}=-0.760305136\) \(a_{74}=+0.076558000\) \(a_{75}=+0.197580542\)
\(a_{76}=-0.825846309\) \(a_{77}=-0.373486247\) \(a_{78}=-0.037911546\) \(a_{79}=+1.490164736\) \(a_{80}=+0.779810922\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.154211946\) \(a_{83}=-1.279030957\) \(a_{84}=+0.258516245\) \(a_{85}=+0.204725423\)
\(a_{86}=+0.042746906\) \(a_{87}=+0.107211253\) \(a_{88}=+0.185748223\) \(a_{89}=+0.603050813\) \(a_{90}=+0.030692316\)
\(a_{91}=+0.262363967\) \(a_{92}=-1.366653765\) \(a_{93}=-0.511278623\) \(a_{94}=+0.027913252\) \(a_{95}=+0.678537332\)
\(a_{96}=-0.193271194\) \(a_{97}=+1.173084279\) \(a_{98}=-0.090169807\) \(a_{99}=-0.274454820\) \(a_{100}=+0.337808653\)

Showing 100 of 750 available coefficients

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