Properties

Level $31$
Weight $0$
Character 31.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 2.98780843925 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.229603827\) \(a_{3}=+0.257503268\) \(a_{4}=-0.947282083\) \(a_{5}=-0.276496853\)
\(a_{6}=-0.059123736\) \(a_{7}=+0.343923725\) \(a_{8}=+0.447103419\) \(a_{9}=-0.933692067\) \(a_{10}=+0.063484736\)
\(a_{11}=-0.996458523\) \(a_{12}=-0.243928232\) \(a_{13}=-0.786753398\) \(a_{14}=-0.078966204\) \(a_{15}=-0.071198843\)
\(a_{16}=+0.844625426\) \(a_{17}=-0.619558368\) \(a_{18}=+0.214379272\) \(a_{19}=+0.843609006\) \(a_{20}=+0.261920515\)
\(a_{21}=+0.088561483\) \(a_{22}=+0.228790691\) \(a_{23}=+0.335445900\) \(a_{24}=+0.115130592\) \(a_{25}=-0.923549490\)
\(a_{26}=+0.180641591\) \(a_{27}=-0.497932027\) \(a_{28}=-0.325792783\) \(a_{29}=+0.977659119\) \(a_{30}=+0.016347527\)
\(a_{31}=+0.179605302\) \(a_{32}=-0.641032649\) \(a_{33}=-0.256591326\) \(a_{34}=+0.142252973\) \(a_{35}=-0.095093828\)
\(a_{36}=+0.884469766\) \(a_{37}=-1.744237493\) \(a_{38}=-0.193695857\) \(a_{39}=-0.202591571\) \(a_{40}=-0.123622688\)
\(a_{41}=-0.251100055\) \(a_{42}=-0.020334056\) \(a_{43}=-0.294399239\) \(a_{44}=+0.943927305\) \(a_{45}=+0.258162918\)
\(a_{46}=-0.077019663\) \(a_{47}=+0.726995816\) \(a_{48}=+0.217493808\) \(a_{49}=-0.881716471\) \(a_{50}=+0.212050498\)
\(a_{51}=-0.159538305\) \(a_{52}=+0.745277397\) \(a_{53}=+1.124226979\) \(a_{54}=+0.114327099\) \(a_{55}=+0.275517646\)
\(a_{56}=+0.153769473\) \(a_{57}=+0.217232076\) \(a_{58}=-0.224474276\) \(a_{59}=-0.808194137\) \(a_{60}=+0.067445388\)
\(a_{61}=+0.171944452\) \(a_{62}=-0.041238065\) \(a_{63}=-0.321118854\) \(a_{64}=-0.697441877\) \(a_{65}=+0.217534838\)
\(a_{66}=+0.058914351\) \(a_{67}=-0.630620069\) \(a_{68}=+0.586896541\) \(a_{69}=+0.086378416\) \(a_{70}=+0.021833907\)
\(a_{71}=-0.046062399\) \(a_{72}=-0.417456915\) \(a_{73}=+0.190248602\) \(a_{74}=+0.400483604\) \(a_{75}=-0.237817012\)
\(a_{76}=-0.799135696\) \(a_{77}=-0.342705727\) \(a_{78}=+0.046515800\) \(a_{79}=-1.691869948\) \(a_{80}=-0.233536272\)
\(a_{81}=+0.805472943\) \(a_{82}=+0.057653534\) \(a_{83}=-0.065955017\) \(a_{84}=-0.083892706\) \(a_{85}=+0.171305939\)
\(a_{86}=+0.067595192\) \(a_{87}=+0.251750418\) \(a_{88}=-0.445520012\) \(a_{89}=+1.930504997\) \(a_{90}=-0.059275194\)
\(a_{91}=-0.270583160\) \(a_{92}=-0.317761891\) \(a_{93}=+0.046248952\) \(a_{94}=-0.166921022\) \(a_{95}=-0.233255235\)
\(a_{96}=-0.165068002\) \(a_{97}=+0.909567838\) \(a_{98}=+0.202445476\) \(a_{99}=+0.930385418\) \(a_{100}=+0.874861885\)

Showing 100 of 546 available coefficients

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