Properties

Level $31$
Weight $0$
Character 31.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 1.68678370214 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.652498641\) \(a_{3}=-1.315687173\) \(a_{4}=-0.574245522\) \(a_{5}=+0.635627439\)
\(a_{6}=+0.858484093\) \(a_{7}=-0.803994122\) \(a_{8}=+1.027193065\) \(a_{9}=+0.731032738\) \(a_{10}=-0.414746041\)
\(a_{11}=-1.465363986\) \(a_{12}=+0.755527469\) \(a_{13}=+0.681660101\) \(a_{14}=+0.524605074\) \(a_{15}=-0.836286869\)
\(a_{16}=-0.095996558\) \(a_{17}=-0.646896572\) \(a_{18}=-0.476997869\) \(a_{19}=-1.523942314\) \(a_{20}=-0.365006210\)
\(a_{21}=+1.057804755\) \(a_{22}=+0.956148008\) \(a_{23}=+1.355606931\) \(a_{24}=-1.351464738\) \(a_{25}=-0.595977754\)
\(a_{26}=-0.444782289\) \(a_{27}=+0.353876772\) \(a_{28}=+0.461690022\) \(a_{29}=+1.222183026\) \(a_{30}=+0.545676049\)
\(a_{31}=-0.179605294\) \(a_{32}=-0.964555442\) \(a_{33}=+1.927960595\) \(a_{34}=+0.422099122\) \(a_{35}=-0.511040722\)
\(a_{36}=-0.419792309\) \(a_{37}=-0.854317489\) \(a_{38}=+0.994370329\) \(a_{39}=-0.896851445\) \(a_{40}=+0.652912069\)
\(a_{41}=-1.473721567\) \(a_{42}=-0.690216172\) \(a_{43}=-0.082022043\) \(a_{44}=+0.841478706\) \(a_{45}=+0.464664516\)
\(a_{46}=-0.884531640\) \(a_{47}=-0.202894290\) \(a_{48}=+0.126301446\) \(a_{49}=-0.353593512\) \(a_{50}=+0.388874758\)
\(a_{51}=+0.851113574\) \(a_{52}=-0.391440278\) \(a_{53}=+0.091504319\) \(a_{54}=-0.230904095\) \(a_{55}=-0.931425566\)
\(a_{56}=-0.825857236\) \(a_{57}=+2.005031414\) \(a_{58}=-0.797472820\) \(a_{59}=+0.260105761\) \(a_{60}=+0.480234080\)
\(a_{61}=-0.559863771\) \(a_{62}=+0.117192268\) \(a_{63}=-0.587746091\) \(a_{64}=+0.725367625\) \(a_{65}=+0.433281854\)
\(a_{66}=-1.257991655\) \(a_{67}=+1.062972604\) \(a_{68}=+0.371477469\) \(a_{69}=-1.783554710\) \(a_{70}=+0.333453476\)
\(a_{71}=-0.389762756\) \(a_{72}=+0.750911873\) \(a_{73}=+0.075514611\) \(a_{74}=+0.557440876\) \(a_{75}=+0.784120355\)
\(a_{76}=+0.875117077\) \(a_{77}=+1.178144092\) \(a_{78}=+0.585194358\) \(a_{79}=+0.701133982\) \(a_{80}=-0.061018067\)
\(a_{81}=-1.196623823\) \(a_{82}=+0.961601209\) \(a_{83}=+0.714757486\) \(a_{84}=-0.607439648\) \(a_{85}=-0.411185308\)
\(a_{86}=+0.053519290\) \(a_{87}=-1.608010554\) \(a_{88}=-1.505211675\) \(a_{89}=-0.835977373\) \(a_{90}=-0.303192913\)
\(a_{91}=-0.548050722\) \(a_{92}=-0.778451242\) \(a_{93}=+0.236304399\) \(a_{94}=+0.132388148\) \(a_{95}=-0.968659522\)
\(a_{96}=+1.269053185\) \(a_{97}=-1.217791991\) \(a_{98}=+0.230719221\) \(a_{99}=-1.071229042\) \(a_{100}=+0.342237597\)

Showing 100 of 1500 available coefficients

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